Help for package pcts

Type:

Package

Title:

Periodically Correlated and Periodically Integrated Time Series

Description:

Classes and methods for modelling and simulation of periodically correlated (PC) and periodically integrated time series. Compute theoretical periodic autocovariances and related properties of PC autoregressive moving average models. Some original methods including Boshnakov & Iqelan (2009) <doi:10.1111/j.1467-9892.2009.00617.x>, Boshnakov (1996) <doi:10.1111/j.1467-9892.1996.tb00281.x>.

Version:

0.15.8

Depends:

R (≥ 3.5.0), methods

Imports:

sarima, Matrix (≥ 1.5-0), BB, PolynomF (≥ 2.0-2), gbutils, zoo, xts, stats4, lagged (≥ 0.2.2), mcompanion (≥ 0.5.8), Rdpack (≥ 0.9), lubridate

Suggests:

testthat, fUnitRoots, knitr, rmarkdown

RdMacros:

Rdpack

LazyData:

yes

URL:

https://geobosh.github.io/pcts/ (doc) https://github.com/GeoBosh/pcts/ (devel)

BugReports:

https://github.com/GeoBosh/pcts/issues

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Collate:

utils.R test1.r PeriodicCalc.R pcstat.R pc00smallutil.r pc02filters.r pc03simu.r acfsums.R pcls.R pcarma_model.R pcarma_acf.R generics.R autocovariances.R classCycle.R pcFilterClasses.R PeriodicClasses.R cyclic.R FittedPeriodicModels.R fitPM.R pcTest.R PeriodicVector.R sim.R optimcore.R trig.R

RoxygenNote:

7.1.1

VignetteBuilder:

knitr

NeedsCompilation:

Packaged:

2025-03-17 09:33:01 UTC; georgi

Author:

Georgi N. Boshnakov

[aut, cre]

Maintainer:

Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk>

Repository:

CRAN

Date/Publication:

2025-03-17 11:00:02 UTC

Periodically Correlated and Periodically Integrated Time Series

Description

Details

The underlying assumption is that the observations are made at regular intervals, such as quarter, month, week, day — or represent data for such intervals — and these intervals are nested into larger periods. In pcts we call the larger period a cycle and its parts seasons. Typical examples of season-cycle timing are months in a year, quarters in a year, days in a week (or business week). The number of seasons in a cycle is called frequency in class "ts" in base R.

Cycles in pcts keep not only the number of seasons (frequency) but other information, such as the names of the seasons and units of seasons. In pcts there are a number of builtin cycle classes for typical cases, as well as provision for creation of custom cycles on the fly. See pcCycle and BuiltinCycle for ways to create cycle objects, and allSeasons for further examples.

Periodic time series can be created with pcts, which accepts as input vectors, matrices and time series objects from base R and some other packages, including zoo and xts. When importing data, the time information is taken from the data and an attempt is made to guess the periodicity from the frequency (for time series objects that have it set) and an analysis of the datetime stamps, if present. pcts also has arguments for specifying the number of seasons or the cycle, as well as the start datetime.

The main periodic time series classes in pcts are PeriodicTS and PeriodicMTS, for univariate and multivariate time series, respectively. Standard base-R time series functions can be used with them directly, see for example window, frequency, cycle, time, deltat, start, end, boxplot, monthplot, na.trim (na.trim is from package zoo).

Methods for plot, summary, print, show, head, tail, and other base-R functions are defined where suitable. Examples can be found in section Examples and in help pages for the corresponding functions, classes and methods.

The naming conventions are as follows. Names of classes generally consists of one or more words. The first letter of each word, is capitalised. Only the first letter of abbreviations for models, such as ARMA, is capitalised. Similarly for generic functions but for them the first word is not capitalised. In a few names PM stands for 'periodic model' and TS for 'time series'.

Significant portion of the code was written in 2005–2007. Many of the functions and classes have been renamed under the above conventions and most of those that are not are not exported but a few still are and they should be considered subject to change.

autocovariances, autocorrelations, partialAutocorrelations and others are one-stop generic functions for computation of properties of time series and models. What to compute is deduced from the type of the object. For models they compute theoretical quantities — periodic or non-periodic, scalar or multivariate. For time series they compute the corresponding sample counterparts.

Author(s)

Georgi N. Boshnakov [aut, cre] (<https://orcid.org/0000-0003-2839-346X>)

Maintainer: Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk>

References

Boshnakov GN (1994). “Periodically Correlated Sequences: Some Properties and Recursions.” Research Report 1, Division of Quality Technology and Statistics, Luleo University, Sweden.

Boshnakov GN (1996). “The asymptotic covariance matrix of the multivariate serial correlations.” Stochastic Process. Appl., 65(2), 251–258. ISSN 0304-4149, doi:10.1016/S0304-4149(96)00104-4.

Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.

Boshnakov GN (1997). “Periodically correlated solutions to a class of stochastic difference equations.” In Csiszar I, Michaletzky G (eds.), Stochastic differential and difference equations (Gyor, 1996), volume 23 of Progr. Systems Control Theory, 1–9. Birkhauser Boston, Boston, MA.

Boshnakov GN (2002). “Multi-companion matrices.” Linear Algebra Appl., 354, 53–83. ISSN 0024-3795, doi:10.1016/S0024-3795(01)00475-X.

Boshnakov GN, Boteva A (1992). “An algorithm for the computation of the theoretical autocovariances of a periodic autoregression process.” Varna.

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Boshnakov GN, Iqelan BM (2012). “Maximum entropy models for general lag patterns.” Journal of Time Series Analysis, 33(1), 112–120. ISSN 1467-9892, doi:10.1111/j.1467-9892.2011.00744.x.

Boshnakov GN, Lambert-Lacroix S (2009). “Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients.” J. Time Series Anal., 30(5), 467–486. doi:10.1111/j.1467-9892.2009.00619.x.

Boshnakov GN, Lambert-Lacroix S (2011). pcme: Maximum entropy estimation of periodically correlated time series. R package version 0.55, https://personalpages.manchester.ac.uk/staff/georgi.boshnakov/Rpackages/.

Boshnakov GN, Lambert-Lacroix S (2012). “A periodic Levinson-Durbin algorithm for entropy maximization.” Computational Statistics & Data Analysis, 56, 15–24. ISSN 0167-9473, doi:10.1016/j.csda.2011.07.001.

Boswijk HP, Franses PH (1996). “Unit roots in periodic autoregressions.” Journal of Time Series Analysis, 17(3), 221–245.

Francq C, Roy R, Saidi A (2011). “Asymptotic properties of weighted least squares estimation in weak parma models.” Journal of Time Series Analysis, 32(6), 699–723.

Franses PH (1996). Periodicity and Stochastic Trends In Economic Time Series. Oxford University Press Inc., New York.

Franses PH, Paap R (2004). Periodic Time Series Models. Oxford University Press Inc., New York.

Grolemund G, Wickham H (2011). “Dates and Times Made Easy with lubridate.” Journal of Statistical Software, 40(3), 1–25. doi:10.18637/jss.v040.i03.

Hipel KW, McLeod AI (1994). Time series modelling of water resources and environmental systems, Developments in water science; 45. London; Amsterdam: Elsevier.

Lambert-Lacroix S (2000). “On periodic autoregressive process estimation.” IEEE Transactions on Signal Processing, 48(6), 1800-1803.

Lambert-Lacroix S (2005). “Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(3), 423-435.

Lancaster P, Tismenetsky M (1985). The theory of matrices, Second edition. Academic Press, New York.

McLeod AI (1993). “Parsimony, model adequacy and periodic correlation in time series forecasting.” Internat. Statist. Rev., 61(3), 387-393.

McLeod AI (1993). “Parsimony, model adequacy and periodic correlation in time series forecasting.” Internat. Statist. Rev., 61(3), 387-393.

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.

McLeod AI (1995). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 16(6), 647-648. doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).

Pagano M (1978). “On periodic and multiple autoregression.” Ann. Statist., 6, 1310-1317.

Examples

data(dataFranses1996) 
class(dataFranses1996) # [1] "mts"    "ts"     "matrix"

pcfr <- pcts(dataFranses1996)

class(pcfr)        # "PeriodicMTS"
nSeasons(pcfr) # 4
allSeasons(pcfr)
allSeasons(pcfr, abb = TRUE)

## subsetting
## one index, x[i], is analogous to lists
pcfr2to4 <- pcfr[2:4]; class(pcfr2to4) # "PeriodicMTS"
pcfr2to2 <- pcfr[2];   class(pcfr2to2) # "PeriodicMTS"
pcfr2    <- pcfr[[2]]; class(pcfr2)    # note '[[', "PeriodicTS"

## data for 1990 quarter 3
pcfr2to4[as_date("1990-07-01")] # note: not "1990-03-01"!
pct1990_Q3 <- Pctime(c(1990, 3), pcCycle(pcfr2to4))
pcfr2to4[pct1990_Q3]

## with empty index, returns the underlying data
dim(pcfr[]) # [1] 148  19
dim(pcfr2to2[]) # 148 1
length(pcfr2[]) # 148 (this is numeric)

summary(pcfr2)
summary(pcfr2to4)
## make the output width shorter
summary(pcfr2to4, row.names = FALSE)
summary(pcfr2to4, row.names = 5) # trim row names to 5 characters

head(pcfr2to4)  # starts with NA's
tail(pcfr2to4)  # some NA's at the end too

## time of first and last data, may be NA's
start(pcfr2to4) # 1955 Q1
end(pcfr2to4)   # 1991 Q4

## time of first nonNA:
availStart(pcfr2)    # 1955 Q1
availStart(pcfr2to4) # 1955 Q1

## time of last nonNA:
availEnd(pcfr[[2]])   # 1991 Q4
availEnd(pcfr[[3]])   # 1987 Q4
availEnd(pcfr[[4]])   # 1990 Q4
## but at least one of them is  available for 1991 Q4, so:
availEnd(pcfr2to4)   # 1991 Q4

## use window() to pick part of the ts by time:
window(pcfr2to4, start = c(1990, 1), end = c(1991, 4))
## drop NA's at the start and end:
window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4))

plot(pcfr2) # the points mark the first season in each cycle
boxplot(pcfr2)
monthplot(pcfr2)

Methods for function`$` in package 'pcts'

Description

Methods for function$ in package 'pcts'.

Methods

signature(x = "PeriodicMTS")

Class BareCycle

Description

Class BareCycle.

Objects from the Class

Objects can be created by calls of the form pcCycle(nseasons) or new("BareCycle", nseasons).

Class "BareCycle" represents the number of seasons and is sufficient for many computations.

Slots

nseasons:: Object of class "integer", the number of seasons.

Extends

Class "BasicCycle", directly.

Methods

initialize: signature(.Object = "BareCycle"): ...
coerce: signature(from = "BareCycle", to = "SimpleCycle"): ...
coerce: signature(from = "BuiltinCycle", to = "BareCycle"): ...
nSeasons: signature(object = "BareCycle"): ...
show: signature(object = "BareCycle"): ...

Author(s)

Georgi N. Boshnakov

Examples

pcCycle(5)
cycle <- new("BareCycle", 5)
identical(new("BareCycle", 5), pcCycle(5)) # TRUE

unitSeason(cycle)
unitCycle(cycle)
allSeasons(cycle)
seqSeasons(cycle)

cycle[]
cycle[3]

## if cycle represents 5-days week one may prefer:
BuiltinCycle(5)

Class BasicCycle

Description

Virtual class "BasicCycle" is a class union that can be used in signatures of methods and classes when any of the cycle classes is admissible as argument or slot.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

[: signature(x = "BasicCycle", i = "ANY", j = "missing", drop = "ANY")
[: signature(x = "BasicCycle", i = "missing", j = "missing", drop = "ANY")
[<-: signature(x = "BasicCycle", i = "ANY", j = "missing", value = "ANY")
[<-: signature(x = "BasicCycle", i = "missing", j = "missing", value = "ANY")
date<-: signature(x = "BasicCycle"): ...
allSeasons: signature(x = "BasicCycle", abb = "ANY")
seqSeasons: signature(x = "BasicCycle")
pcCycle: signature(x = "BasicCycle", type = "character"): ...
pcCycle: signature(x = "BasicCycle", type = "missing"): ...
pcts: signature(x = "matrix", nseasons = "BasicCycle"): ...
pcts: signature(x = "numeric", nseasons = "BasicCycle"): ...

Author(s)

Georgi N. Boshnakov

Examples

showClass("BasicCycle")

Class `"BuiltinCycle"` and its subclasses in package 'pcts'

Description

Class "BuiltinCycle" and its subclasses in package 'pcts'.

Objects from the Class

Class "BuiltinCycle" is a virtual Class: no objects may be created from it. Class "BuiltinCycle" has several built-in cycle subclasses. Objects from the subclasses can be created by calls of the form new("className", first, ...), where "className" is the name of the subclass. The optional argument first can be used to designate a season to be considered first in the cycle, by default the first.

The function BuiltinCycle provides a more convenient way to generate objects from subclasses of class "BuiltinCycle". Its argument is the number of seasons.

These classes are effectively unmodifiable, but the user can convert them to other cycle classes, e.g. class "SimpleCycle", and adapt as needed.

The subclasses of "BuiltinCycle" have definitions for all methods promised by its superclass "BasicCycle".

Currently, the following builtin classes are defined:

Name	Description	nSeasons
`"DayWeekCycle"`	weekdays	7
`"QuarterYearCycle"`	quarters in a year	4
`"MonthYearCycle"`	months in a year	12
`"Every30MinutesCycle"`	half-hour intervals in a day	48
`"OpenCloseCycle"`	start/end of a working day	2

There is also a class "FiveDayWeekCycle" but it is deprecated and will be removed in the near future. Use BuiltinCycle(5) to create objects with equivalent functionality.

Slots

The class "BuiltinCycle" and its subclasses have a single common slot:

first:: Object of class "integer", the index of the season to be treated as the first in a cycle.

Extends

Class "BuiltinCycle" extends class "BasicCycle", directly.

Classes "DayWeekCycle", "Every30MinutesCycle", "FiveDayWeekCycle", "OpenCloseCycle" and "QuarterYearCycle" extend:

Class "BuiltinCycle", directly. Class "BasicCycle", by class "BuiltinCycle", distance 2.

Methods

Functions with methods for this class:

coerce: signature(from = "BuiltinCycle", to = "BareCycle"): ...
coerce: signature(from = "BuiltinCycle", to = "SimpleCycle"): ...
initialize: signature(.Object = "BuiltinCycle"): ...
show: signature(object = "BuiltinCycle"): ...

The functions to extract properties from objects from the builtin cycle classes have identical signatures (except for the name of the class). For example, for "QuarterYearCycle" the methods are as follows:

allSeasons: signature(x = "QuarterYearCycle", abb = "logical"): ...
allSeasons: signature(x = "QuarterYearCycle", abb = "missing"): ...
nSeasons: signature(object = "QuarterYearCycle"): ...
unitCycle: signature(x = "QuarterYearCycle"): ...
unitSeason: signature(x = "QuarterYearCycle"): ...

The methods for the remaining builtin classes are the same with "QuarterYearCycle" replaced suitably.

Author(s)

Georgi N. Boshnakov

Examples

## class "DayWeekCycle"
dwcycle <- BuiltinCycle(7) # new("DayWeekCycle")

unitSeason(dwcycle)
unitCycle(dwcycle)

allSeasons(dwcycle)
dwcycle[] # same

allSeasons(dwcycle, abb = TRUE)
dwcycle[ , abb = TRUE] # same

dwcycle[2]
dwcycle[2, abb = TRUE]

seqSeasons(dwcycle)

## start the week on Sunday
dws <- BuiltinCycle(7, first = 7) # new("DayWeekCycle", first = 7)
dws[1] # "Sunday"
allSeasons(dws)

## class "Every30MinutesCycle"
cyc48 <- BuiltinCycle(48) # new("Every30MinutesCycle")
nSeasons(cyc48)
allSeasons(cyc48)

## class "FiveDayWeekCycle" is deprecated, use the equivalent:
fdcycle <- BuiltinCycle(5)

unitSeason(fdcycle)
unitCycle(fdcycle)

allSeasons(fdcycle)
fdcycle[] # same

allSeasons(fdcycle, abb = TRUE)
fdcycle[ , abb = TRUE] # same

fdcycle[2]
fdcycle[2, abb = TRUE]

seqSeasons(fdcycle)

## class "MonthYearCycle"
mycycle <- BuiltinCycle(12) # new("MonthYearCycle")

unitSeason(mycycle)
unitCycle(mycycle)

allSeasons(mycycle)
mycycle[ ] # same

allSeasons(mycycle, , abb = TRUE)
mycycle[ , abb = TRUE] # same

mycycle[2]
mycycle[2, abb = TRUE]

seqSeasons(mycycle)

## class "OpenCloseCycle"
opcycle <- new("OpenCloseCycle")

unitSeason(opcycle)
unitCycle(opcycle)

allSeasons(opcycle)
opcycle[ , abb = FALSE] # same

allSeasons(opcycle, abb = FALSE)
opcycle[] # same

opcycle[2]
opcycle[2, abb = TRUE]

seqSeasons(opcycle)

## class "QuarterYearCycle"
qycycle <- new("QuarterYearCycle")

unitSeason(qycycle)
unitCycle(qycycle)

allSeasons(qycycle)
qycycle[] # same

allSeasons(qycycle, abb = TRUE)
qycycle[ , abb = TRUE] # same

qycycle[2]
qycycle[2, abb = TRUE]

seqSeasons(qycycle)

Create objects from class Cyclic

Description

Create objects from class Cyclic.

Usage

Cyclic(cycle, start = NULL, ...)

## S3 method for class 'Cyclic'
as.Date(x, ...)

## S3 method for class 'Cyclic'
date(x)

## S3 method for class 'PeriodicTimeSeries'
as.Date(x, ...)

Arguments

cycle

a cycle object, a positive integer giving the number of seasons, or any other object that can be used to create a cycle with pcCycle(x, ...).

start

a cycle-season pair, a datetime object, a Date object or any object that can be converted to datetime with as_datetime(start).

...

for Cyclic, arguments passed to pcCycle, used only if cycle is not from a cycle class.

x

a Cyclic object

Value

for Cyclic, an object from class "Cyclic"

Examples

## bare bone Cyclic starting at Cycle 1, season 1
Cyclic(4)    
Cyclic(4, c(1,1)) # same

## with quarter/year cycle
qu <- Cyclic(BuiltinCycle(4), start = c(2020, 1))
start(qu)
as_datetime(qu)

date(qu) <- c(2009, 2)
qu

ap <- pcts(AirPassengers)
as.Date(ap)

Class `"Cyclic"`

Description

Class "Cyclic"

Objects from the Class

Objects can be created by calls of the form new("Cyclic", ...).

Slots

cycle:: Object of class "BasicCycle" ~~
pcstart:: Object of class "ANY" ~~

Methods

allSeasons: signature(x = "Cyclic", abb = "ANY"): ...
allSeasons<-: signature(x = "Cyclic"): ...
as_date: signature(x = "Cyclic"): ...
coerce: signature(from = "PeriodicMTS", to = "Cyclic"): ...
coerce: signature(from = "PeriodicTS", to = "Cyclic"): ...
coerce<-: signature(from = "PeriodicMTS", to = "Cyclic"): ...
coerce<-: signature(from = "PeriodicTS", to = "Cyclic"): ...
date<-: signature(x = "Cyclic"): ...
nSeasons: signature(object = "Cyclic"): ...
nTicks: signature(x = "Cyclic"): ...
pcCycle: signature(x = "Cyclic", type = "ANY"): ...
seqSeasons: signature(x = "Cyclic"): ...
show: signature(object = "Cyclic"): ...
unitCycle: signature(x = "Cyclic"): ...
unitCycle<-: signature(x = "Cyclic"): ...
unitSeason: signature(x = "Cyclic"): ...
unitSeason<-: signature(x = "Cyclic"): ...

Examples

showClass("Cyclic")

Class FittedPeriodicArModel

Description

Class FittedPeriodicArModel.

Objects from the Class

Objects can be created by calls of the form new("FittedPeriodicArModel", ar, ma, sigma2, ...).

Slots

asyCov:: Object of class "ANY" ~~
sigma2:: Object of class "numeric" ~~
ar:: Object of class "PeriodicArFilter" ~~
ma:: Object of class "PeriodicMaFilter" ~~
center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
theTS:: Object of class "PeriodicTS" ~~
ns:: Object of class "numeric" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Class "PeriodicArModel", directly. Class "PeriodicArmaModel", by class "PeriodicArModel", distance 2. Class "VirtualPeriodicArmaModel", by class "PeriodicArModel", distance 3. Class "PeriodicArmaSpec", by class "PeriodicArModel", distance 3. Class "VirtualPeriodicFilterModel", by class "PeriodicArModel", distance 4. Class "VirtualPeriodicStationaryModel", by class "PeriodicArModel", distance 4. Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArModel", distance 5. Class "VirtualPeriodicMeanModel", by class "PeriodicArModel", distance 5.

Methods

show: signature(object = "FittedPeriodicArModel"): ...
summary: signature(object = "FittedPeriodicArModel"): ...
as_pcarma_list: signature(object = "FittedPeriodicArModel"): ...

Class FittedPeriodicArmaModel

Description

Class FittedPeriodicArmaModel in package pcts

Objects from the Class

Objects can be created by calls of the form new("FittedPeriodicArmaModel", ..., mean).

Slots

ar:: Object of class "PeriodicBJFilter" ~~
ma:: Object of class "PeriodicSPFilter" ~~
modelCycle:: Object of class "BasicCycle" ~~
center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
sigma2:: Object of class "numeric" ~~
theTS:: Object of class "PeriodicTS" ~~
asyCov:: Object of class "ANY" ~~
ns:: Object of class "numeric" ~~

Extends

Class "PeriodicArmaModel", directly. Class "FittedPM", directly. Class "VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2. Class "PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2. Class "VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3. Class "VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3. Class "PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3. Class "PeriodicInterceptSpec", by class "PeriodicArmaModel", distance 3. Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4. Class "VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4. Class "VirtualArmaFilter", by class "PeriodicArmaModel", distance 4. Class "ModelCycleSpec", by class "PeriodicArmaModel", distance 4. Class "InterceptSpec", by class "PeriodicArmaModel", distance 4. Class "VirtualPeriodicModel", by class "PeriodicArmaModel", distance 5. Class "VirtualMonicFilter", by class "PeriodicArmaModel", distance 5.

Methods

as_pcarma_list: signature(object = "FittedPeriodicArmaModel"): ...
show: signature(object = "FittedPeriodicArmaModel"): ...

Fraser River at Hope, mean monthly flow

Description

Mean monthly flow (cms) of Fraser River From March 1912 to December 2017, recorded by Fraser River at Hope station.

Usage

data("Fraser2017")

Format

A time series (class "ts") with frequency 12, starting from January 1912 (the first two data values are NA) to December 2017.

Details

Dataset Fraser2017 is an extention of dataset "Fraser" in package "pear". The latter runs upto December 1990 (not the documented December 1991). At the time of writing this package "pear" is archived on CRAN, which is the main reason to include the dataset (with the added benefit of almost 30 years of additional data).

Source

https://wateroffice.ec.gc.ca/

Examples

data(Fraser2017)

fr <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12))
## all.equal(as.numeric(fr), as.numeric(pear::Fraser)) # TRUE
## all.equal(tsp(fr), tsp(pear::Fraser))               # TRUE

Class LegacyPeriodicFilterModel

Description

Class LegacyPeriodicFilterModel.

Objects from the Class

Objects can be created by calls of the form new("LegacyPeriodicFilterModel", ...).

Slots

intercept:: Object of class "numeric" ~~
arFilter:: Object of class "PeriodicArFilter" ~~
maFilter:: Object of class "PeriodicMaFilter" ~~
scalesq:: Object of class "numeric" ~~
jordan:: Object of class "ANY" ~~

Extends

Class "VirtualPeriodicFilterModel", directly.

Methods

No methods defined with class "LegacyPeriodicFilterModel" in the signature.

Class ModelCycleSpec

Description

Class ModelCycleSpec.

Objects from the Class

Objects can be created by calls of the form new("ModelCycleSpec", ...).

Slots

modelCycle:: Object of class "BasicCycle" ~~

Methods

modelCycle: signature(object = "ModelCycleSpec"): ...
modelCycle<-: signature(object = "ModelCycleSpec"): ...

Class PartialCycle

Description

Class PartialCycle

Objects from the Class

Objects can be created by calls of the form new("PartialCycle", ...).

Partial cycles are often created implicitly when subsetting time series using window() with argument seasons, see the examples.

Slots

orig:: the parent class of the partial cycle, an object inheriting from class "BasicCycle".
subindex:: an integer vector specifying the seasons to include in the partial cycle.

Extends

Class "BasicCycle", directly.

Methods

allSeasons: signature(x = "PartialCycle", abb = "logical"): ...
allSeasons: signature(x = "PartialCycle", abb = "missing"): ...
nSeasons: signature(object = "PartialCycle"): ...
unitCycle: signature(x = "PartialCycle"): ...
unitSeason: signature(x = "PartialCycle"): ...
show: signature(object = "PartialCycle"): ...

Examples

dwc <- new("DayWeekCycle")
dwc
allSeasons(dwc)

## a five day week cycle
dwc5 <- new("PartialCycle", orig = dwc, subindex = 1:5)
dwc5
allSeasons(dwc5)

weekend <- new("PartialCycle", orig = dwc, subindex = 6:7)
weekend
allSeasons(weekend)

ap <- pcts(AirPassengers)

## take data for the summer months (in Northern hemisphere)
ap7to9 <- window(ap, seasons = 7:9)
## the above implicitly creates a partial cycle
ap7to9
allSeasons(ap7to9)

Class PartialPeriodicAutocorrelations

Description

Class PartialPeriodicAutocorrelations.

Objects from the Class

Objects can be created by calls of the form new("PartialPeriodicAutocorrelations", ..., data).

Slots

modelCycle:: Object of class "BasicCycle" ~~
data:: Object of class "Lagged" ~~

Extends

Class "ModelCycleSpec", directly. Class "FlexibleLagged", directly. Class "VirtualPeriodicAutocorrelations", directly. Class "Lagged", by class "FlexibleLagged", distance 2. Class "VirtualPeriodicModel", by class "VirtualPeriodicAutocorrelations", distance 2.

Methods

show: signature(object = "PartialPeriodicAutocorrelations"): ...

Convert between Pctime and datetime objects

Description

Class "Pctime" is an S3 class inheriting from the base R datetime class "POSIXct". It has methods for conversion between datetimes and the pcts cycle-season pairs, as well as convenience methods for a few other functions.

Usage

Pctime(x, cycle, ...)

as_Pctime(x, ...)

## S3 method for class 'Pctime'
x[i, j, drop = TRUE]

## S3 method for class 'Pctime'
x[[..., drop = TRUE]]

## S3 method for class 'Cyclic'
as_Pctime(x, ...)

Arguments

x

for Pctime, numeric vector, matrix with two columns, or any object that is or can be converted to datetime. For the other functions see Details.

cycle

a positive integer, cycle object, or missing.

i

subscript

j

noi used

drop

not used

...

further argument for methods.

Details

Pctime represents periodic times with cycle specification contained in attribute "cycle". It is basically datetime (inheriting from "POSIXct") with additional attribute(s).

For printing Pctime objects are shown as cycle-season pairs. To print in other formats, just convert them using as_datetime or other suitable function. Note though that some cycles in pcts do not have natural datetime representation. For them, Pctime sets it arbitrarilly as the number of seconds from a origin.

The seasons in cycle-season pairs are numbered from one to the number of seasons. Names and abbreviations are used when available and this is the case for all builtin cycles and partial cycles obtained from them.

The cycles in cycle-season pairs are numbered from a starting point. For years, it is what is expected. For cycles representing weeks, week 1 is the first ISO week of 1970, so c(1,1) corresponds to 1969-12-29. For some other cycle classes c(1,1) also corresponds to the first time in the first ISO week of 1970.

Subsetting with "[" keeps the Pctime class, while "[[" returns a datetime object. Other standard functions work with Pctime objects, as well, including seq.

A common source of frustration is the accidental use of as.Date or as_date, instead of as.POSIXlt or as_datetime. These four are often equivalent, most notably for monthly, quarterly and daily observations but, in general, conversion to dates drops the fractional day part of a datetime.

The default time zone is UTC. Other time zones can be used since the calculations use standard datetime and date functions from base R and package lubridate (Grolemund and Wickham 2011), but currently this has not been tested.

Value

for Pctime, an object from S3 class Pctime

References

Grolemund G, Wickham H (2011). “Dates and Times Made Easy with lubridate.” Journal of Statistical Software, 40(3), 1–25. doi:10.18637/jss.v040.i03.

Examples

## a bare bone date for four seasons
pct4 <- Pctime(c(2020, 2), pcCycle(4))
pct4

## quarterly cycle
Pctime("2020-04-01", BuiltinCycle(4))
pctQ <- Pctime(c(2020, 2), BuiltinCycle(4))  # same
pctQ

## day-in-week cycle
## c(1, 1) is the start of the first ISO week of 1970
weekW1S1 <- Pctime(c(1, 1), BuiltinCycle(7))  # W1 Mon
weekW1S1
as_datetime(weekW1S1)

Pctime("1970-01-01", BuiltinCycle(7)) #  W1 Thu
pctW1Th <- Pctime(c(1, 4), BuiltinCycle(7))  # same
pctW1Th

Pctime("2020-04-01", BuiltinCycle(7))
pctW2623Wed <- Pctime(c(2623, 3), BuiltinCycle(7))  # same
pctW2623Wed
as_datetime(pctW2623Wed)

## Monday-Friday week - a partial cycle derived from DayOfWeekCycle
BuiltinCycle(5)
pctMF <- Pctime("2020-04-03", BuiltinCycle(5)) # Fri
seq(pctMF, length.out = 10) # note: Sat, Sun are skipped

Pctime("2020-04-04", BuiltinCycle(5)) # Sat, not in the cycle

## monthly cycle
Pctime("2020-04-01", BuiltinCycle(12))
pctY2020Apr <- Pctime(c(50, 4), BuiltinCycle(12))  # same
pctY2020Apr
as_datetime(pctW2623Wed)

## Pctime can hold a vector of times
ap <- pcts(AirPassengers)
aptime <- Pctime(ap)              #  as_Pctime(ap)
aptime[1:12] # keep Pctime class
aptime[1]

aptime[[1]] # drop Pctime class

head(aptime)
tail(aptime)

apdates <- as_datetime(ap)
head(apdates)
tail(apdates)

Class PeriodicArModel

Description

Class PeriodicArModel.

Objects from the Class

Objects can be created by calls of the form new("PeriodicArModel", ar, ma, sigma2, ...).

Slots

sigma2:: Object of class "numeric" ~~
ar:: Object of class "PeriodicArFilter" ~~
ma:: Object of class "PeriodicMaFilter" ~~
center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Class "PeriodicArmaModel", directly. Class "VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2. Class "PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2. Class "VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3. Class "VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3. Class "PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3. Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4. Class "VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.

Methods

autocovariances: signature(x = "PeriodicArModel", maxlag = "ANY"): ...
coerce: signature(from = "PeriodicArmaModel", to = "PeriodicArModel"): ...
fitPM: signature(model = "PeriodicArModel", x = "ANY"): ...
fitPM: signature(model = "PeriodicArModel", x = "PeriodicMTS"): ...
fitPM: signature(model = "PeriodicArModel", x = "PeriodicTS"): ...
partialCoefficients: signature(x = "PeriodicArModel"): ...
show: signature(object = "PeriodicArModel"): ...

Create objects from class PeriodicArModel

Description

Create objects from class PeriodicArModel

Usage

PeriodicArModel(object, ...)

Arguments

object

an object, can have one of a number of classes.

...

further arguments for methods.

Details

PeriodicArModel creates objects from class PeriodicArModel. This is a generic function with dispatch methods on the first argument.

Value

an object from class "PeriodicArModel"

Methods

signature(object = "matrix"): "object" gives the coefficients, one row per season.
signature(object = "numeric"): "object" gives the model order. Its length is taken to be the number of seasons. The coefficients are set to NA.
signature(object = "PeriodicMonicFilterSpec")
signature(object = "VirtualPeriodicArmaModel")
signature(object = "PeriodicMonicFilterSpec")
signature(object = "VirtualPeriodicArmaModel")

Class `"PeriodicArmaFilter"`

Description

Class PeriodicArmaFilter.

Objects from the Class

Objects can be created by calls of the form new("PeriodicArmaFilter", ..., ar, ma, nseasons).

Slots

ar:: Object of class "PeriodicBJFilter" ~~
ma:: Object of class "PeriodicSPFilter" ~~

Extends

Class "VirtualArmaFilter", directly. Class "VirtualMonicFilter", by class "VirtualArmaFilter", distance 2.

Methods

coerce: signature(from = "PeriodicArmaFilter", to = "PeriodicArFilter"): ...
coerce: signature(from = "PeriodicArmaFilter", to = "PeriodicMaFilter"): ...
initialize: signature(.Object = "PeriodicArmaFilter"): ...
maxLag: signature(object = "PeriodicArmaFilter"): ...
show: signature(object = "PeriodicArmaFilter"): ...

Class PeriodicArmaModel

Description

Class PeriodicArmaModel.

Objects from the Class

Objects can be created by calls of the form new("PeriodicArmaModel", ar, ma, sigma2, ...).

Slots

sigma2:: Object of class "numeric" ~~
ar:: Object of class "PeriodicArFilter" ~~
ma:: Object of class "PeriodicMaFilter" ~~
center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Class "VirtualPeriodicArmaModel", directly. Class "PeriodicArmaSpec", directly. Class "VirtualPeriodicFilterModel", by class "VirtualPeriodicArmaModel", distance 2. Class "VirtualPeriodicStationaryModel", by class "VirtualPeriodicArmaModel", distance 2. Class "PeriodicArmaFilter", by class "PeriodicArmaSpec", distance 2. Class "VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicArmaModel", distance 3. Class "VirtualPeriodicMeanModel", by class "VirtualPeriodicArmaModel", distance 3.

Methods

autocovariances: signature(x = "PeriodicArmaModel", maxlag = "ANY"): ...
coerce: signature(from = "PeriodicArmaModel", to = "list"): ...
coerce: signature(from = "PeriodicArmaModel", to = "PeriodicArModel"): ...
show: signature(object = "PeriodicArmaModel"): ...

Class PeriodicArmaSpec

Description

Class PeriodicArmaSpec.

Objects from the Class

Objects can be created by calls of the form new("PeriodicArmaSpec", pcmean, pcintercept, ...).

Slots

sigma2:: Object of class "numeric" ~~
ar:: Object of class "PeriodicArFilter" ~~
ma:: Object of class "PeriodicMaFilter" ~~
center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Class "PeriodicArmaFilter", directly.

Methods

Functions with methods for this class:

initialize: signature(.Object = "PeriodicArmaSpec"): ...
show: signature(object = "PeriodicArmaSpec"): ...

Class PeriodicAutocorrelations

Description

Class PeriodicAutocorrelations.

Objects from the Class

Objects can be created by calls of the form new("PeriodicAutocorrelations", ..., data).

Slots

modelCycle:: Object of class "BasicCycle" ~~
data:: Object of class "Lagged" ~~

Extends

Methods

plot: signature(x = "PeriodicAutocorrelations", y = "missing"): ...

Class PeriodicAutocovariances

Description

Class PeriodicAutocovariances.

Objects from the Class

Objects can be created by calls of the form new("PeriodicAutocovariances", ..., data).

Slots

modelCycle:: Object of class "BasicCycle" ~~
data:: Object of class "Lagged" ~~

Extends

Class "ModelCycleSpec", directly. Class "FlexibleLagged", directly. Class "VirtualPeriodicAutocovariances", directly. Class "Lagged", by class "FlexibleLagged", distance 2. Class "VirtualPeriodicModel", by class "VirtualPeriodicAutocovariances", distance 2.

Methods

autocorrelations: signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
partialAutocorrelations: signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...

Class PeriodicBJFilter

Description

A class for filters following the Box-Jenkins sign convention

Objects from the Class

Objects can be created by calls of the form new("PeriodicBJFilter", coef, order, ...).

Slots

coef:: Object of class "matrix" ~~
order:: Object of class "numeric" ~~

Extends

Class "PeriodicMonicFilterSpec", directly. Class "VirtualBJFilter", directly. Class "VirtualMonicFilterSpec", by class "PeriodicMonicFilterSpec", distance 2. Class "VirtualMonicFilter", by class "VirtualBJFilter", distance 2.

Methods

filterCoef: signature(object = "PeriodicBJFilter", convention = "character"): ...
coerce: signature(from = "matrix", to = "PeriodicBJFilter"): ...
coerce: signature(from = "PeriodicBJFilter", to = "PeriodicSPFilter"): ...
coerce: signature(from = "PeriodicSPFilter", to = "PeriodicBJFilter"): ...
filterPoly: signature(object = "PeriodicBJFilter"): ...
filterPolyCoef: signature(object = "PeriodicBJFilter"): ...
show: signature(object = "PeriodicBJFilter"): ...

Author(s)

Georgi N. Boshnakov

Examples

## a toy filter of order c(3, 3, 3, 3) and 4 seasons
co <- matrix(c(1, 1, 0,
               2, 2, 2,
               3, 0, 0,
               4, 4, 4), nrow = 4, ncol = 3)

## these are equivalent:
bj1 <- new("PeriodicBJFilter", coef = co)
bj1b <- new("PeriodicBJFilter", coef = co, order = 3)
bj1c <- new("PeriodicBJFilter", coef = co, order = c(3, 3, 3, 3))
identical(bj1b, bj1c) # TRUE
identical(bj1, bj1b) # FALSE but only because classbj1@order is "integer"

    
## a more refined spec. for the order:
show( new("PeriodicBJFilter", coef = co, order = c(2, 3, 1, 3)) )

## as()
show( as(co, "PeriodicBJFilter") )
show( as(co, "PeriodicSPFilter") )

## change the sign convention:
sp1 <- as(bj1, "PeriodicSPFilter")

## the two parameterisations have different signs:
bj1
sp1

## nevertheless, bj1 and sp1 represent the same filter
filterPoly(bj1)
filterPoly(sp1)
identical(filterPoly(bj1), filterPoly(sp1)) # TRUE

filterPolyCoef(bj1)
filterPolyCoef(sp1)
identical(filterPolyCoef(bj1), filterPolyCoef(sp1)) # TRUE

filterOrder(bj1)
nSeasons(bj1)

Class PeriodicFilterModel

Description

Class PeriodicFilterModel.

Objects from the Class

Objects can be created by calls of the form new("PeriodicFilterModel", pcmean, pcintercept, ...).

Slots

center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
sigma2:: Object of class "numeric" ~~
ar:: Object of class "PeriodicArFilter" ~~
ma:: Object of class "PeriodicMaFilter" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Class "VirtualPeriodicFilterModel", directly. Class "PeriodicArmaSpec", directly. Class "PeriodicArmaFilter", by class "PeriodicArmaSpec", distance 2.

Methods

Functions with methods for this class:

show: signature(object = "PeriodicFilterModel"): ...

Class PeriodicIntegratedArmaSpec

Description

Class PeriodicIntegratedArmaSpec.

Objects from the Class

Objects can be created by calls of the form new("PeriodicIntegratedArmaSpec", ...).

Slots

pcmodel:: Object of class "PeriodicArmaModel" ~~

Methods

sigmaSq: signature(object = "PeriodicIntegratedArmaSpec"): ...
nSeasons: signature(object = "PeriodicIntegratedArmaSpec"): ...

Class PeriodicInterceptSpec

Description

Class PeriodicInterceptSpec.

Objects from the Class

Objects can be created by calls of the form new("PeriodicInterceptSpec", ...).

Slots

center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
sigma2:: Object of class "numeric" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Class "numeric", from data part. Class "vector", by class "numeric", distance 2. Class "index", by class "numeric", distance 2. Class "replValue", by class "numeric", distance 2. Class "numLike", by class "numeric", distance 2. Class "number", by class "numeric", distance 2. Class "atomicVector", by class "numeric", distance 2.

Methods

sigmaSq: signature(object = "PeriodicInterceptSpec"): ...
allSeasons: signature(x = "PeriodicInterceptSpec", abb = "ANY"): ...
initialize: signature(.Object = "PeriodicInterceptSpec"): ...
nSeasons: signature(object = "PeriodicInterceptSpec"): ...
show: signature(object = "PeriodicInterceptSpec"): ...

Class `"PeriodicMTS"`

Description

Class "PeriodicMTS" is the main class for multivariate periodic time series in package "pcts".

Objects from the Class

Objects can be created by calls of the form new("PeriodicMTS", ...) but it is recommended to use the function pcts in most cases.

Slots

.Data:: Object of class "matrix", the core data. Several functions can be used to extract it in various formats, see Vec.
cycle:: Object of class "BasicCycle", representing the seasonal information, see pcCycle.
pcstart:: Object of class "ANY", the time of the first observation.

Extends

Class "PeriodicTimeSeries", directly. Class "matrix", from data part. Class "Cyclic", by class "PeriodicTimeSeries", distance 2. Class "array", by class "matrix", distance 2. Class "mMatrix", by class "matrix", distance 2. Class "optionalMatrix-class", by class "matrix", distance 2. Class "structure", by class "matrix", distance 3. Class "vector", by class "matrix", distance 4, with explicit coerce.

Methods

$: signature(x = "PeriodicMTS"): ...
[: signature(x = "PeriodicMTS", i = "missing", j = "missing", drop = "ANY"): ...
[: signature(x = "PeriodicMTS", i = "ANY", j = "missing", drop = "ANY"): ...
[: signature(x = "PeriodicMTS", i = "ANY", j = "ANY", drop = "ANY"): ...
[: signature(x = "PeriodicMTS", i = "AnyDateTime", j = "missing", drop = "ANY"): ...
[: signature(x = "PeriodicMTS", i = "AnyDateTime", j = "ANY", drop = "ANY"): ...
[[: signature(x = "PeriodicMTS", i = "ANY", j = "ANY"): ...
coerce: signature(from = "mts", to = "PeriodicMTS"): ...
coerce: signature(from = "PeriodicMTS", to = "ts"): ...
coerce: signature(from = "ts", to = "PeriodicMTS"): ...
coerce: signature(from = "PeriodicMTS", to = "Cyclic"): ...
coerce<-: signature(from = "PeriodicMTS", to = "Cyclic"): ...
plot: signature(x = "PeriodicMTS", y = "missing"): ...
show: signature(object = "PeriodicMTS"): ...
summary: signature(object = "PeriodicMTS"): ...
fitPM: signature(model = "PeriodicArModel", x = "PeriodicMTS"): ...
pcApply: signature(object = "PeriodicMTS"): ...
pcMean: signature(object = "PeriodicMTS"): ...

Examples

pcfr <- pcts(dataFranses1996)
colnames(pcfr)[4] # "GermanyGNP"

## extracting single time series as univariate 
class(pcfr[[4]]) # "PeriodicTS"
identical(pcfr[[4]], pcfr$GermanyGNP )     # TRUE
identical(pcfr[[4]], pcfr[["GermanyGNP"]]) # TRUE
plot(pcfr[[4]])

## ... and as multivariate
pcfr[4] #  "PeriodicMTS"
plot(pcfr[4])

## extracting more than one time series
plot(pcfr[2:4])
summary(pcfr[2:4])

pcfr2 <- pcfr[[2]]
plot(pcfr2)

Class `"PeriodicMTS_ts"`

Description

Class "PeriodicMTS_ts" is a periodic class holding multivariate "ts" objects.

Objects from the Class

Objects can be created by calls of the form new("PeriodicMTS_ts", x, ...).

Slots

.Data:: Object of class "vector" ~~
cycle:: Object of class "BasicCycle" ~~
pcstart:: Object of class "ANY" ~~
tsp:: Object of class "numeric" ~~
.S3Class:: Object of class "character" ~~

Extends

Class "PeriodicTimeSeries", directly. Class "ts", directly. Class "Cyclic", by class "PeriodicTimeSeries", distance 2. Class "structure", by class "ts", distance 2. Class "oldClass", by class "ts", distance 2. Class "vector", by class "ts", distance 3, with explicit coerce.

Methods

coerce: signature(from = "ts", to = "PeriodicMTS_ts"): ...
initialize: signature(.Object = "PeriodicMTS_ts"): ...

Class `"PeriodicMTS_zooreg"`

Description

Class "PeriodicMTS_zooreg" is a periodic class holding multivariate "zooreg" objects.

Objects from the Class

Objects can be created by calls of the form new("PeriodicMTS_zooreg", ...).

Slots

cycle:: Object of class "BasicCycle" ~~
.S3Class:: Object of class "character" ~~
pcstart:: Object of class "ANY" ~~

Extends

Methods

No methods defined with class "PeriodicMTS_zooreg" in the signature.

Class PeriodicMaModel

Description

Class PeriodicMaModel.

Objects from the Class

Objects can be created by calls of the form new("PeriodicMaModel", ar, ma, sigma2, ...).

Slots

sigma2:: Object of class "numeric" ~~
ar:: Object of class "PeriodicArFilter" ~~
ma:: Object of class "PeriodicMaFilter" ~~
center:: Object of class "numeric" ~~
intercept:: Object of class "numeric" ~~
modelCycle:: Object of class "BasicCycle" ~~

Extends

Methods

show: signature(object = "PeriodicMaModel"): ...

Class PeriodicSPFilter

Description

A class for filters following the signal processing sign convention.

Objects from the Class

Objects can be created by calls of the form new("PeriodicSPFilter", coef, order, ...).

Slots

coef:: Object of class "matrix" ~~
order:: Object of class "numeric" ~~

Extends

Class "PeriodicMonicFilterSpec", directly. Class "VirtualSPFilter", directly. Class "VirtualMonicFilterSpec", by class "PeriodicMonicFilterSpec", distance 2. Class "VirtualMonicFilter", by class "VirtualSPFilter", distance 2.

Methods

coerce: signature(from = "matrix", to = "PeriodicSPFilter"): ...
coerce: signature(from = "PeriodicBJFilter", to = "PeriodicSPFilter"): ...
coerce: signature(from = "PeriodicSPFilter", to = "PeriodicBJFilter"): ...
filterCoef: signature(object = "PeriodicSPFilter", convention = "character"): ...
filterPoly: signature(object = "PeriodicSPFilter"): ...
filterPolyCoef: signature(object = "PeriodicSPFilter"): ...
show: signature(object = "PeriodicSPFilter"): ...

Author(s)

Georgi N. Boshnakov

Examples

## see "PeriodicBJFilter-class" for examples

Class `"PeriodicTS"`

Description

Class "PeriodicTS" is the main class for univariate periodic time series in package "pcts".

Objects from the Class

Objects can be created from numeric vectors and objects from other time series classes by calling pcts (recommended in most cases).

It is possible also to use calls of the form new("PeriodicTS", ...). This is more useful in programming.

Slots

.Data:: Object of class "numeric", the core data. Several functions can be used to extract it in various formats, see Vec.
cycle:: Object of class "BasicCycle", representing the seasonal information, see pcCycle.
pcstart:: Object of class "ANY", the time of the first observation.

Extends

Class "PeriodicTimeSeries", directly. Class "numeric", from data part. Class "Cyclic", by class "PeriodicTimeSeries", distance 2. Class "vector", by class "numeric", distance 2. Class "index", by class "numeric", distance 2. Class "replValue", by class "numeric", distance 2. Class "numLike", by class "numeric", distance 2. Class "number", by class "numeric", distance 2. Class "atomicVector", by class "numeric", distance 2. Class "numericVector", by class "numeric", distance 2. Class "replValueSp", by class "numeric", distance 3. Class "Mnumeric", by class "numeric", distance 3.

Methods

[: signature(x = "PeriodicTS", i = "AnyDateTime", j = "missing", drop = "ANY"): ...
[: signature(x = "PeriodicTS", i = "missing", j = "missing", drop = "ANY"): ...
coerce: signature(from = "mts", to = "PeriodicTS"): ...
coerce: signature(from = "PeriodicTS", to = "ts"): ...
coerce: signature(from = "ts", to = "PeriodicTS"): ...
coerce: signature(from = "PeriodicTS", to = "Cyclic"): ...
coerce<-: signature(from = "PeriodicTS", to = "Cyclic"): ...
plot: signature(x = "PeriodicTS", y = "missing"): ...
show: signature(object = "PeriodicTS"): ...
summary: signature(object = "PeriodicTS"): ...
autocovariances: signature(x = "PeriodicTS", maxlag = "ANY"): ...
fitPM: signature(model = "PeriodicArModel", x = "PeriodicTS"): ...
pcApply: signature(object = "PeriodicTS"): ...
pcMean: signature(object = "PeriodicTS"): ...

Class `"PeriodicTS_ts"`

Description

Class "PeriodicTS_ts" is a periodic class holding "ts" objects.

Objects from the Class

Objects can be created by calls of the form new("PeriodicTS_zooreg", ...).

Objects from the Class

Objects can be created by calls of the form new("PeriodicTS_ts", x, ...).

Slots

.Data:: Object of class "vector" ~~
cycle:: Object of class "BasicCycle" ~~
tsp:: Object of class "numeric" ~~
.S3Class:: Object of class "character" ~~
pcstart:: Object of class "ANY" ~~

Extends

Methods

coerce: signature(from = "ts", to = "PeriodicTS_ts"): ...
initialize: signature(.Object = "PeriodicTS_ts"): ...

Class `"PeriodicTS_zooreg"`

Description

Class "PeriodicTS_zooreg" is a periodic class holding "zooreg" objects.

Objects from the Class

Objects can be created by calls of the form new("PeriodicTS_zooreg", ...).

Slots

cycle:: Object of class "BasicCycle" ~~
.S3Class:: Object of class "character" ~~
pcstart:: Object of class "ANY" ~~

Extends

Methods

No methods defined with class "PeriodicTS_zooreg" in the signature.

Class PeriodicTimeSeries

Description

Class PeriodicTimeSeries.

Objects from the Class

A virtual Class: No objects may be created from it.

PeriodicTimeSeries is the root class for the periodic time series classes in package "pcts". It can be used in signatures for methods that can handle objcets from any of them.

Slots

cycle:: Object of class "BasicCycle".
pcstart:: Object of class "ANY".

Extends

Class "Cyclic", directly.

Methods

as_date: signature(x = "PeriodicTimeSeries"): ...
as_datetime: signature(x = "PeriodicTimeSeries"): ...
autocorrelations: signature(x = "PeriodicTimeSeries", maxlag = "ANY", lag_0 = "missing"): ...
pcTest: signature(x = "PeriodicTimeSeries", nullmodel = "character"): ...
head: signature(x = "PeriodicTimeSeries"): ...
nTicks: signature(x = "PeriodicTimeSeries"): ...
pcCycle: signature(x = "PeriodicTimeSeries", type = "character"): ...
pcCycle: signature(x = "PeriodicTimeSeries", type = "missing"): ...
tail: signature(x = "PeriodicTimeSeries"): ...

Class PeriodicVector

Description

Objects and methods for class PeriodicVector.

Usage

PeriodicVector(x, period = length(x))

Arguments

x

the values for inidices from 1 to period, numeric.

period

the period, defaults to length(x).

Details

A p-periodic vector, X, is such that X_{i+pk} = X_i for any integers i,k.

Class PeriodicVector stores the values of X_1,\ldots,X_p and provides indexing methods for extracting and setting its elements.

Value

an object from class "PeriodicVector"

Objects from the Class

Objects can be created by calls of the form new("PeriodicVector", ...) or more conveniently by using "PeriodicVector()".

Slots

.Data:: Object of class "numeric" ~~
period:: Object of class "numeric" ~~

Extends

Class "numeric", from data part. Class "vector", by class "numeric", distance 2. Class "atomicVector", by class "numeric", distance 2. Class "index", by class "numeric", distance 2.

Class "numLike", by class "numeric", distance 2.

Class "number", by class "numeric", distance 2. Class "replValue", by class "numeric", distance 2.

Methods

"PeriodicVector" methods are defined for "[" and "[<-". Arithmetic operations just inherit the recycling rules from "numeric".

[: signature(x = "PeriodicVector", i = "ANY", j = "ANY", drop = "ANY"): ...
[: signature(x = "PeriodicVector", i = "ANY", j = "missing", drop = "ANY"): ...
[: signature(x = "PeriodicVector", i = "missing", j = "ANY", drop = "ANY"): ...
[: signature(x = "PeriodicVector", i = "missing", j = "missing", drop = "ANY"): ...
[<-: signature(x = "PeriodicVector", i = "ANY", j = "ANY", value = "ANY"): ...
[<-: signature(x = "PeriodicVector", i = "missing", j = "ANY", value = "ANY"): ...

Author(s)

Georgi N. Boshnakov

Examples

PeriodicVector(1:4, period = 4)
PeriodicVector(1:4) ## same
new("PeriodicVector", 1:4, period = 4)

## if period is given but x is missing, the vector is filled with NA's
PeriodicVector(period = 4)

## this throws error, since length(x) != period:
##    PeriodicVector(1:3, period = 4)

## extract
x <- PeriodicVector(1:4)
x[3:12]
x[c(3, 7, 11, 15)]

# any indices in (-Inf, Inf) work
x[0]
x[-3:0]

## "[<-" works on the underling vector
x[1] <- 11; x

## modulo indexing works also in assignments:
x[5] <- 21; x

## empty index returns the underlying vector
x[]

## the recycling rule applies on assignment
x[] <- 9; x
x[] <- 1:2; x

## this gives warning, as for numeric vectors
##     x[] <- 8:1
## compare:
##     x <- 1:4
##     x[] <- 8:1

## arithmetic works as usual:
2 * x
x + 1:4
## x + 1:3 # warning - '... a multiple ...'

Class PiPeriodicArModel

Description

Class PiPeriodicArModel.

Objects from the Class

Objects can be created by calls of the form new("PiPeriodicArModel", ...).

Slots

piorder:: Object of class "numeric" ~~
picoef:: Object of class "matrix" ~~
pcmodel:: Object of class "PeriodicArmaModel" ~~

Extends

Class "PiPeriodicArmaModel", directly. Class "VirtualPeriodicFilterModel", by class "PiPeriodicArmaModel", distance 2. Class "PeriodicIntegratedArmaSpec", by class "PiPeriodicArmaModel", distance 2.

Methods

fitPM: signature(x = "ANY", model = "PiPeriodicArModel"): ...
fitPM: signature(model = "PiPeriodicArModel", x = "ANY"): ...
show: signature(object = "PiPeriodicArModel"): ...

Class PiPeriodicArmaModel

Description

Class PiPeriodicArmaModel.

Objects from the Class

Objects can be created by calls of the form new("PiPeriodicArmaModel", ...).

Slots

piorder:: Object of class "numeric" ~~
picoef:: Object of class "matrix" ~~
pcmodel:: Object of class "PeriodicArmaModel" ~~

Extends

Class "VirtualPeriodicFilterModel", directly. Class "PeriodicIntegratedArmaSpec", directly.

Methods

show: signature(object = "PiPeriodicArmaModel"): ...

Class PiPeriodicMaModel

Description

Class PiPeriodicMaModel.

Objects from the Class

Objects can be created by calls of the form new("PiPeriodicMaModel", ...).

Slots

piorder:: Object of class "numeric" ~~
picoef:: Object of class "matrix" ~~
pcmodel:: Object of class "PeriodicArmaModel" ~~

Extends

Methods

No methods defined with class "PiPeriodicMaModel" in the signature.

Class SLTypeMatrix

Description

Class SLTypeMatrix is a virtual class for classes that can hold objects with season-lag conventions.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "SLTypeMatrix" in the signature.

Examples

showClass("SLTypeMatrix")

Class SamplePeriodicAutocorrelations

Description

Class SamplePeriodicAutocorrelations.

Objects from the Class

Objects can be created by calls of the form new("SamplePeriodicAutocorrelations", ..., data).

Slots

modelCycle:: Object of class "BasicCycle" ~~
data:: Object of class "Lagged" ~~
n:: Object of class "numeric" ~~
varnames:: Object of class "character" ~~
objectname:: Object of class "character" ~~

Extends

Class "PeriodicAutocorrelations", directly. Class "Fitted", directly. Class "ModelCycleSpec", by class "PeriodicAutocorrelations", distance 2. Class "FlexibleLagged", by class "PeriodicAutocorrelations", distance 2. Class "VirtualPeriodicAutocorrelations", by class "PeriodicAutocorrelations", distance 2. Class "Lagged", by class "PeriodicAutocorrelations", distance 3. Class "VirtualPeriodicModel", by class "PeriodicAutocorrelations", distance 3.

Methods

No methods defined with class "SamplePeriodicAutocorrelations" in the signature.

Class SamplePeriodicAutocovariances

Description

Class SamplePeriodicAutocovariances.

Objects from the Class

Objects can be created by calls of the form new("SamplePeriodicAutocovariances", ..., data).

Slots

modelCycle:: Object of class "BasicCycle" ~~
data:: Object of class "Lagged" ~~
n:: Object of class "numeric" ~~
varnames:: Object of class "character" ~~
objectname:: Object of class "character" ~~

Extends

Class "PeriodicAutocovariances", directly. Class "Fitted", directly. Class "ModelCycleSpec", by class "PeriodicAutocovariances", distance 2. Class "FlexibleLagged", by class "PeriodicAutocovariances", distance 2. Class "VirtualPeriodicAutocovariances", by class "PeriodicAutocovariances", distance 2. Class "Lagged", by class "PeriodicAutocovariances", distance 3. Class "VirtualPeriodicModel", by class "PeriodicAutocovariances", distance 3.

Methods

autocorrelations: signature(x = "SamplePeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...

Class SiPeriodicArModel

Description

Class SiPeriodicArModel.

Objects from the Class

Objects can be created by calls of the form new("SiPeriodicArModel", ...).

Slots

iorder:: Object of class "numeric" ~~
siorder:: Object of class "numeric" ~~
pcmodel:: Object of class "PeriodicArmaModel" ~~

Extends

Class "SiPeriodicArmaModel", directly. Class "VirtualPeriodicFilterModel", by class "SiPeriodicArmaModel", distance 2. Class "PeriodicIntegratedArmaSpec", by class "SiPeriodicArmaModel", distance 2.

Methods

fitPM: signature(model = "SiPeriodicArModel", x = "ANY"): ...
show: signature(object = "SiPeriodicArModel"): ...

Class SiPeriodicArmaModel

Description

Class SiPeriodicArmaModel.

Objects from the Class

Objects can be created by calls of the form new("SiPeriodicArmaModel", ...).

Slots

iorder:: Object of class "numeric" ~~
siorder:: Object of class "numeric" ~~
pcmodel:: Object of class "PeriodicArmaModel" ~~

Extends

Class "VirtualPeriodicFilterModel", directly. Class "PeriodicIntegratedArmaSpec", directly.

Methods

No methods defined with class "SiPeriodicArmaModel" in the signature.

Class SiPeriodicMaModel

Description

Class SiPeriodicMaModel.

Objects from the Class

Objects can be created by calls of the form new("SiPeriodicMaModel", ...).

Slots

iorder:: Object of class "numeric" ~~
siorder:: Object of class "numeric" ~~
pcmodel:: Object of class "PeriodicArmaModel" ~~

Extends

Methods

No methods defined with class "SiPeriodicMaModel" in the signature.

Class SimpleCycle

Description

Class SimpleCycle.

Objects from the Class

Objects can be created by calls of the form new("SimpleCycle", nseasons, seasons, first).

In addition to number of seasons, class "SimpleCycle" holds also seasons' names and the index of the season to be treated as the first in a cycle.

Slots

seasons:: Object of class "character", the names of the seasons.
nseasons:: Object of class "integer", number of seasons.
cycle:: Object of class "character" ~~
season:: Object of class "character" ~~
abbreviated:: Object of class "character" ~~

Extends

Class "BareCycle", directly. Class "BasicCycle", directly.

Methods

allSeasons: signature(x = "SimpleCycle", abb = "ANY"): ...
allSeasons<-: signature(x = "SimpleCycle"): ...
coerce: signature(from = "BareCycle", to = "SimpleCycle"): ...
coerce: signature(from = "BuiltinCycle", to = "SimpleCycle"): ...
initialize: signature(.Object = "SimpleCycle"): ...
show: signature(object = "SimpleCycle"): ...
unitCycle: signature(x = "SimpleCycle"): ...
unitCycle<-: signature(x = "SimpleCycle"): ...
unitSeason: signature(x = "SimpleCycle"): ...
unitSeason<-: signature(x = "SimpleCycle"): ...

Author(s)

Georgi N. Boshnakov

Examples

showClass("SimpleCycle")

Class SubsetPM

Description

Class "SubsetPM" - subset PAR models with trigonometric parameterisation.

Objects from the Class

Objects can be created by calls of the form new("SubsetPM", ...) but they are typically created by model fitting functions, see the examples.

Slots

theTS:: "ANY", the time series to which the model is fitted.
period:: "integer", the period.
order:: "integer", the order.
findex:: "function".
harmonics:: "integer", Fourier harmonics to include in the model.
call:: "call", the call used to fit the model.
other:: "namedList".

Methods

coef: signature(object = "SubsetPM"): ...
fitted: signature(object = "SubsetPM"): ...
residuals: signature(object = "SubsetPM"): ...
show: signature(object = "SubsetPM"): ...
vcov: signature(object = "SubsetPM"): ...

Examples

pcfr4 <- pcts(dataFranses1996)[[4]]
x4 <- as.numeric(window(pcfr4, start = availStart(pcfr4), end = availEnd(pcfr4)))

## without 'harmonics' these models are equivalent
tmpfit  <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE)
tmpfitL <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE)

## for comparison
tmpfitP <- pclsdf(x4, 4, 1:2, sintercept = FALSE)

## with intercept
tmpfitc  <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE,
    sintercept = TRUE)
tmpfitcn  <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE,
    sintercept = structure(TRUE, merge = TRUE))
tmpfitLc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag",
    verbose = FALSE, sintercept = TRUE)

coef(tmpfitc, matrix = TRUE)
coef(tmpfitcn, matrix = TRUE)
coef(tmpfitLc, matrix = TRUE)

coef(tmpfitc)
coef(tmpfitcn)
coef(tmpfitLc)

coef(tmpfit)
coef(tmpfitL)

## convert to PAR coefficients:
coef(tmpfitc,  type = "PAR", matrix = TRUE)
coef(tmpfitcn, type = "PAR", matrix = TRUE)
coef(tmpfitLc, type = "PAR", matrix = TRUE)

coef(tmpfitL, type = "PAR", matrix = TRUE)



predict(tmpfitc, n.ahead = 4)
predict(tmpfitcn, n.ahead = 4)

sqrt(diag((vcov(tmpfitL))))
e <- residuals(tmpfitL)
fi <-  fitted(tmpfitL)

Core data of periodic time series

Description

Extract the core data from a periodic time series as a vector, matrix or array.

Usage

Vec(x, ...)

tsMatrix(x, ...)

tsVector(x, ...)

tsVec(x, ...)

pcMatrix(x, ...)

pcArray(x, ndim = 3, ...)

pctsArray(x, ndim = 3, ...)

Arguments

x

an object.

...

further arguments for methods.

ndim

currently not used.

Details

These functions give the core data in various common forms.

The data values can be extracted as a vector from a periodic time series object, say x, with as.vector(x) or as(x, "vector"). For multivariate time series the vector returned by as.vector(x) (or as(x, "vector")) is equivalent to as.vector(as.matrix(x)).

Similarly, as.matrix() and as(x, "matrix") extract the data as a matrix containing one column per variable.

Vec() is like as.vector() but the result is a matrix with one column (column vector). The default does literally this. Thus both, Vec() and as.vector(), implement the Vec operation from matrix calculus but the latter returns the result as a vector, not matrix.

The most common representation of data in statistics is matrix-like with one column per variable. The descriptions of algorithms for multivariate time series however usually define the vector of observations at a given time to be a column vector. In particular, implementations of the Kalman filter often require precisely this arrangement. In that case the data matrix is the transposed of the more common one and the vectorising operation stacks the observations, not the variables.

The functions tsMatrix(), tsVector() and tsVec() provide the analogues of as.vector(), as.matrix() and Vec() for the “transposed” arrangement.

These functions may look redundant since they are simple combinations of the above and traspose operations. Having functions makes for more readable programming. They may be more efficient, as well, for example if the underlying time series class stores the data in the transposed format.

pcMatrix() and pcArray() also give the core data. Effectively, they give an additional dimension to the seasons. The season becomes the first dimension since for column oriented data the season changes fastest. pcMatrix is most suitable for univariate time series, pcArray() for multivariate. Note that pcArray() easily extends to multiple periodicities although currently (2019-04-19) there are no methods that exploit this.

For univariate time series, in the matrix returned by pcMatrix() each row represents the data for one season and each column for one cycle. For multivariate time series, the matrices for each variable are put next to each other.

pcArray() returns the data as an array, whose last dimension corresponds to variables. In the default case the array is 3-dimensonal with dimensions (season, year, variable).

pctsArray() is a variant of pcArray() corresponding to the arrangement of tsMatrix(). The ordering of the dimensions here is (variable, season, cycle).

Value

vector, matrix or array, as indicated by the name of the function and described in section ‘Details’.

Author(s)

Georgi N. Boshnakov

Examples

## window to make number of years different from number of months
ap <- pcts(window(AirPassengers, start = c(1956, 1)))
class( as.vector(ap)    )
class( as(ap, "vector") )

dim( as.matrix(ap)    )
dim( as(ap, "matrix") )

dim( tsMatrix(ap) )

class( tsVector(ap) ) 
dim(   tsVec(ap)    ) 

dim( pcMatrix(ap)   )
dim( pcArray(ap)    )
dim( pctsArray(ap)  )

dfr <- pcts(dataFranses1996)
dim(dfr)                     # c(148, 19)
nSeasons(dfr)                # 4

length(as.vector(dfr))

all.equal(as.vector(dfr)[1:148],       as.matrix(dfr)[ , 1]) # TRUE
all.equal(tsVector(dfr)[1:19],  unname(as.matrix(dfr)[1, ])) # TRUE

dim( as.matrix(dfr) ) # c(148, 19)
dim( tsMatrix(dfr)  ) # c(19, 148)
all.equal(tsMatrix(dfr)[ , 1],  as.matrix(dfr)[1, ]) # TRUE

dim( Vec(dfr)   ) 
dim( tsVec(dfr) ) 
all.equal(tsVec(dfr)[1:19],  unname(as.matrix(dfr)[1, ])) # TRUE

dim( pcMatrix(dfr)   ) # c(4, 703), one row for each season
dim( pcArray(dfr)    ) # c(4, 37, 19), note: 703 == 37*19   

dim( pctsArray(dfr)  ) # c(19, 4, 37), note: 703 == 37*19

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

Objects can be created by calls of the form new("VirtualPeriodicArModel", ...).

Extends

Class "VirtualPeriodicArmaModel", directly. Class "VirtualPeriodicFilterModel", by class "VirtualPeriodicArmaModel", distance 2. Class "VirtualPeriodicStationaryModel", by class "VirtualPeriodicArmaModel", distance 2. Class "VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicArmaModel", distance 3. Class "VirtualPeriodicMeanModel", by class "VirtualPeriodicArmaModel", distance 3.

Methods

No methods defined with class "VirtualPeriodicArModel" in the signature.

Class VirtualPeriodicArmaModel

Description

Class VirtualPeriodicArmaModel.

Objects from the Class

Objects can be created by calls of the form new("VirtualPeriodicArmaModel", ...).

Extends

Class "VirtualPeriodicFilterModel", directly. Class "VirtualPeriodicStationaryModel", directly. Class "VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicStationaryModel", distance 2. Class "VirtualPeriodicMeanModel", by class "VirtualPeriodicStationaryModel", distance 2.

Methods

PeriodicArModel: signature(object = "VirtualPeriodicArmaModel"): ...

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "VirtualPeriodicModel", directly.

Methods

No methods defined with class "VirtualPeriodicAutocorrelations" in the signature.

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

[: signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "missing", drop = "ANY"): ...
[: signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "numeric", drop = "ANY"): ...
[: signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "missing", drop = "ANY"): ...
[: signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "numeric", drop = "ANY"): ...
maxLag: signature(object = "VirtualPeriodicAutocovarianceModel"): ...
autocorrelations: signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "missing", lag_0 = "ANY"): ...
autocorrelations: signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "numeric", lag_0 = "ANY"): ...

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "VirtualPeriodicModel", directly.

Methods

autocorrelations: signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
autocovariances: signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY"): ...
backwardPartialCoefficients: signature(x = "VirtualPeriodicAutocovariances"): ...
backwardPartialVariances: signature(x = "VirtualPeriodicAutocovariances"): ...
partialAutocorrelations: signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "ANY"): ...
partialAutocovariances: signature(x = "VirtualPeriodicAutocovariances"): ...
partialCoefficients: signature(x = "VirtualPeriodicAutocovariances"): ...
partialVariances: signature(x = "VirtualPeriodicAutocovariances"): ...
pc.bU: signature(x = "VirtualPeriodicAutocovariances"): ...
pc.fL: signature(x = "VirtualPeriodicAutocovariances"): ...
pc.phis2: signature(x = "VirtualPeriodicAutocovariances"): ...

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "VirtualPeriodicFilterModel" in the signature.

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

Objects can be created by calls of the form new("VirtualPeriodicMaModel", ...).

Extends

Methods

No methods defined with class "VirtualPeriodicMaModel" in the signature.

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "VirtualPeriodicMeanModel" in the signature.

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

allSeasons: signature(x = "VirtualPeriodicModel", abb = "ANY"): ...
nSeasons: signature(object = "VirtualPeriodicModel"): ...
seqSeasons: signature(x = "VirtualPeriodicModel"): ...
unitCycle: signature(x = "VirtualPeriodicModel"): ...
unitSeason: signature(x = "VirtualPeriodicModel"): ...

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "VirtualPeriodicMonicFilter" in the signature.

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

Objects can be created by calls of the form new("VirtualPeriodicStationaryModel", ...).

Extends

Class "VirtualPeriodicAutocovarianceModel", directly. Class "VirtualPeriodicMeanModel", directly.

Methods

No methods defined with class "VirtualPeriodicStationaryModel" in the signature.

Dummy title

Description

~~ Dummy description ~~

Objects from the Class

Objects can be created by calls of the form new("VirtualPeriodicWhiteNoiseModel", ...).

Extends

Class "VirtualPeriodicStationaryModel", directly. Class "VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicStationaryModel", distance 2. Class "VirtualPeriodicMeanModel", by class "VirtualPeriodicStationaryModel", distance 2.

Methods

No methods defined with class "VirtualPeriodicWhiteNoiseModel" in the signature.

Index assignments for objects from classes in package pcts

Description

Index assignments for objects from classes in package pcts.

Methods

signature(x = "PeriodicVector", i = "ANY", j = "ANY", value = "ANY")
signature(x = "PeriodicVector", i = "missing", j = "ANY", value = "ANY")
signature(x = "BasicCycle", i = "ANY", j = "missing", value = "ANY")
signature(x = "BasicCycle", i = "missing", j = "missing", value = "ANY")
signature(x = "PeriodicAutocovarianceModel", i = "ANY", j = "ANY", value = "ANY")

Author(s)

Georgi N. Boshnakov

Indexing of objects from classes in package pcts

Description

Indexing of objects from classes in package pcts.

Methods

signature(x = "BasicCycle", i = "ANY", j = "missing", drop = "ANY")
signature(x = "BasicCycle", i = "missing", j = "missing", drop = "ANY")
signature(x = "PeriodicMTS", i = "ANY", j = "missing", drop = "ANY")
signature(x = "PeriodicMTS", i = "missing", j = "missing", drop = "ANY")
signature(x = "PeriodicVector", i = "ANY", j = "ANY", drop = "ANY")
signature(x = "PeriodicVector", i = "ANY", j = "missing", drop = "ANY")
signature(x = "PeriodicVector", i = "missing", j = "ANY", drop = "ANY")
signature(x = "PeriodicVector", i = "missing", j = "missing", drop = "ANY")
signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "missing", drop = "ANY")
signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing", j = "numeric", drop = "ANY")
signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "missing", drop = "ANY")
signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "numeric", drop = "ANY")
signature(x = "PeriodicTS", i = "missing", j = "missing", drop = "ANY")
signature(x = "PeriodicMTS", i = "ANY", j = "ANY", drop = "ANY")
signature(x = "PeriodicMTS", i = "AnyDateTime", j = "ANY", drop = "ANY")
signature(x = "PeriodicMTS", i = "AnyDateTime", j = "missing", drop = "ANY")
signature(x = "PeriodicTS", i = "AnyDateTime", j = "missing", drop = "ANY")

Author(s)

Georgi N. Boshnakov

Methods for function`[[` in package 'pcts'

Description

Methods for function`[[` in package 'pcts'.

Methods

signature(x = "PeriodicMTS", i = "ANY", j = "ANY")
signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric", j = "ANY")

Get names of seasons

Description

Functions and methods fo get names of seasons and related quantities for objects from the cycle, periodic time series classes and other objects for which the concepts are defined.

Usage

unitSeason(x)
unitCycle(x)
seqSeasons(x)
allSeasons(x, abb = FALSE, prefix = "S", ...)

unitSeason ( x, ... ) <- value
unitCycle ( x, ... ) <- value
allSeasons ( x, abb, ... ) <- value

## S4 replacement method for signature 'SimpleCycle'
allSeasons(x, abb, prefix, ...) <- value

## S4 replacement method for signature 'Cyclic'
allSeasons(x, abb = FALSE, ...) <- value

Arguments

x

a cycle, time series or other object for which the concept of seasons is defined.

abb

if TRUE give the abbreviated names of the seasons.

prefix

use this prefix for automatically generated names of seasons.

...

further arguments for methods.

value

a character string

Details

The cycle classes, i.e. classes inheriting from class BasicCycle, provide common functionality. In particular, they guarantee that the functions described in this topic are available. These functions work also for the periodic time series classes and may be defined for other classes where they make sense.

Methods

Methods for allSeasons():

signature(x = "BasicCycle", abb = "ANY")
signature(x = "DayWeekCycle", abb = "logical")
signature(x = "DayWeekCycle", abb = "missing")
signature(x = "MonthYearCycle", abb = "logical")
signature(x = "MonthYearCycle", abb = "missing")
signature(x = "OpenCloseCycle", abb = "logical")
signature(x = "OpenCloseCycle", abb = "missing")
signature(x = "QuarterYearCycle", abb = "logical")
signature(x = "QuarterYearCycle", abb = "missing")
signature(x = "SimpleCycle", abb = "ANY")
signature(x = "Cyclic", abb = "ANY")
signature(x = "Every30MinutesCycle", abb = "logical")
signature(x = "Every30MinutesCycle", abb = "missing")
signature(x = "VirtualPeriodicModel", abb = "ANY")

Author(s)

Georgi N. Boshnakov

Examples

opcycle <- new("OpenCloseCycle")
## convert to SimpleCycle to change some names
siopcycle <- as(opcycle, "SimpleCycle")
## siopcycle inherits names from opcycle
unitSeason(siopcycle)             # "Season"
unitCycle(siopcycle)              # "Cycle"
allSeasons(siopcycle)             # "Open"  "Close"
allSeasons(siopcycle, abb = TRUE) # "O" "C"

allSeasons(siopcycle) <- c("Day", "Night")
allSeasons(siopcycle) # now: "Day"   "Night"
## change also abbreviations
allSeasons(siopcycle, abb = TRUE) <- c("D", "N")
allSeasons(siopcycle, abb = TRUE) # now: "D" "N"

seasons <- new("SimpleCycle", 4)
unitSeason(seasons)             # "Season"
unitCycle(seasons)              # "Cycle"
allSeasons(seasons)
allSeasons(seasons, abb = TRUE) 

unitCycle(seasons) <- "Year"
unitCycle(seasons)
allSeasons(seasons) <- c("Winter", "Spring", "Summer", "Autumn")
allSeasons(seasons)
allSeasons(seasons, abb = TRUE) <- c("Win", "Spr", "Sum", "Aut")
allSeasons(seasons, abb = TRUE)

## change autumn to Fall
allSeasons(seasons)[4] <- "Fall"
allSeasons(seasons, abb = TRUE)[4] <- "Fal"
allSeasons(seasons)
allSeasons(seasons, abb = TRUE)

## indexing of cycle objects is equivalent to allSeasons.
seasons[]
seasons[ , abb = TRUE]

seasons[4] <- "Herbst"
seasons

unitCycle(seasons) <- "Jahre"
unitCycle(seasons)
unitSeason(seasons) <- "Jahreszeit"
seasons[] <- c("Winter", "Frueling", "Sommer", "Herbst")
seasons[ , abb = TRUE] <- c("W", "F", "S", "H")
seasons[]
seasons

Replace methods for as_date in package pcts

Description

Replace methods for as_date in package pcts.

Methods

signature(x = "PeriodicTimeSeries")
signature(x = "ANY")
signature(x = "character")
signature(x = "Cyclic")
signature(x = "numeric")
signature(x = "POSIXt")

Methods for as_datetime in package pcts

Description

Methods for as_datetime in package pcts.

Methods

signature(x = "PeriodicTimeSeries")

Compute autocorrelations and periodic autocorrelations

Description

Methods for computation of autocorrelations and periodic autocorrelations.

Methods

signature(x = "numeric", maxlag = "ANY", lag_0 = "missing")
signature(x = "PeriodicTimeSeries", maxlag = "ANY", lag_0 = "missing")
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")
signature(x = "SamplePeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")
signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")
signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "ANY", lag_0 = "missing")

Examples

## periodic ts object => peridic acf
autocorrelations(pcts(AirPassengers), maxlag = 10)

## for "ts" or "numeric" objects the default is non-periodic acf
autocorrelations(AirPassengers, maxlag = 10) 
autocorrelations(as.numeric(AirPassengers))
## argument 'nseasons' forces periodic acf
autocorrelations(AirPassengers, maxlag = 10, nseasons = 12)
autocorrelations(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)

Compute autocovariances and periodic autocovariances

Description

Methods for the generic function autocovariances(), which computes autocovariances meaningful for the first argument. For objects representing time series, it computes sample autocovariances (univariate, multivariate, periodic, as appropriate). For objects representing models, it computes the relevant theoretical autocovariances.

Methods

signature(x = "matrix", maxlag = "ANY")
signature(x = "numeric", maxlag = "ANY")
signature(x = "PeriodicArmaModel", maxlag = "ANY")
signature(x = "PeriodicArModel", maxlag = "ANY")
signature(x = "PeriodicAutocovarianceModel", maxlag = "ANY")
signature(x = "PeriodicTS", maxlag = "ANY")
signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY"): If maxlag is missing or equal to maxLag(x), x is returned unchanged. Otherwise the number of available lags is adjusted to maxlag.

Examples

## periodic ts object => peridic acvf
autocovariances(pcts(AirPassengers), maxlag = 10)

## for "ts" or "numeric" objects the default is non-periodic acvf
autocovariances(AirPassengers, maxlag = 10) 
autocovariances(as.numeric(AirPassengers))
## argument 'nseasons' forces periodic acvf
autocovariances(AirPassengers, maxlag = 10, nseasons = 12)
autocovariances(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)

Time of first or last non-NA value

Description

Time of first or last non-NA value.

Usage

availStart(x, any = TRUE)

availEnd(x, any = TRUE)

Arguments

x

a time series or similar object

any

logical flag for multivariate objects. The default TRUE requests the first/last index containing any non-NA value. FALSE requires that all values at the first/last index must be non-NA.

Details

The time is given as a cycle-season pair.

Argument any is meaningful only for multivariate objects. Its name is short for "the first/last index for which any of the values (ie at least one) is non-NA". any = FALSE is taken to mean that the index is the first/last for which all values are non-NA.

The functions can be used together with windows to trim NA's from the beginning and/or end of the data. As an alternative we provide also methods for periodic time series methods for zoo:na.trim, see the examples below.

Value

numeric, length 2

Examples

tipi <- pcts(dataFranses1996[ , "USTotalIPI"])
start(tipi)
end(tipi)
head(tipi)
tail(tipi)

tipi <- window(tipi, start = availStart(tipi), end = availEnd(tipi))
start(tipi)
end(tipi)
plot(tipi)

pcfr <- pcts(dataFranses1996)

pcfr2to4 <- pcfr[2:4]
head(pcfr2to4)
tail(pcfr2to4)
## time of first and last data, can be NA's
start(pcfr2to4) # 1955 Q1
end(pcfr2to4)   # 1991 Q4

## time of first nonNA:
availStart(pcfr[[2]]) # 1960 Q1
availStart(pcfr2to4)  # 1960 Q1

## time of last nonNA:
availEnd(pcfr[[2]])   # 1991 Q4
availEnd(pcfr[[3]])   # 1987 Q4
availEnd(pcfr[[4]])   # 1990 Q4
## but at least one of them is  available for 1991 Q4, so:
availEnd(pcfr2to4)   # 1991 Q4
## this requests the time of the last full record:
availEnd(pcfr2to4, any = FALSE)   # 1987 Q4

pcfr2to4a <- window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4))
head(pcfr2to4a)
tail(pcfr2to4a, 20)

## trim NA's from both ends, up to the firsxst/last full record:
pcfr2to4b <- window(pcfr2to4, start = availStart(pcfr2to4, FALSE),
                              end = availEnd(pcfr2to4, FALSE))

## TODO: need a better example here since the first non-NA value for all
##     ts in pcfr2to4 is at the same

## alternatively, use na.trim(), the default for is.na is "any"
pcpres <- window(pcts(presidents), end = c(1972, 4))

availStart(pcpres) # 1945 2
availEnd(pcpres)   # 1972 2

both <- na.trim(pcpres) # same as "both"
identical(na.trim(pcpres), both) # TRUE
head(both, 7)
tail(both)
head(na.trim(pcpres, "left"), 7)
tail(na.trim(pcpres, "right"))

cguk <- pcfr[c("CanadaUnemployment", "GermanyGNP", "UKTotalInvestment")]
availStart(cguk)
availStart(cguk, TRUE) # same

availStart(cguk, FALSE)

availEnd(cguk)
availEnd(cguk, TRUE) # same

availEnd(cguk, FALSE)


na.trim(cguk)
head( na.trim(cguk, sides = "left") )
tail( na.trim(cguk, sides = "right") )

head( na.trim(cguk, sides = "left", is.na = "all") )
tail( na.trim(cguk, sides = "right", is.na = "all") )

Compute periodic backward partial coefficients

Description

Methods for computation of periodic backward partial coefficients.

Methods

signature(x = "VirtualPeriodicAutocovariances")

Compute periodic backward partial variances

Description

Compute periodic backward partial variances.

Methods

signature(x = "VirtualPeriodicAutocovariances")

Example data from Franses (1996)

Description

A multivariate time series containing the data used in examples by Franses (1996).

Usage

data("dataFranses1996")

Format

A multivariate quarterly time series.

Details

Each column is a quarterly time series. The time series start and end at different times, so NA's are used to align them in a single multivariate time series. Detailed account of the sources of the data is given by @FransesB1; Data Appendix), p. 214.

year

(column 1)

The time formatted as ⁠yyyy.Q⁠, where ⁠yyyy⁠ is the year and ⁠Q⁠ is the quarter (one of 1, 2, 3 or 4.). This column was part of the original data but is not really needed here since the time series object contains the time information.

USTotalIPI

(column 2)

Total Industrial Production Index for the United States (1985 = 100), 1960.1–1991.4.

CanadaUnemployment

(column 3)

Unemployment in Canada, measured in 1000 persons, 1960.1 - 1987.4.

GermanyGNP

(column 4)

Real GNP in Germany, 1960.1 - 1990.4 .

UKTotalInvestment

(column 5)

Real Total Investment in the United Kindom, 1955.1 - 1988.4.

SA_USTotalIPI

(column 6) Seasonally adjusted USTotalIPI.

SA_CanadaUnemployment

(column 7)

Seasonally adjusted CanadaUnemployment.

SA_GermanyGNP

(column 8)

Seasonally adjusted GermanyGNP.

UKGDP

(column 9)

United Kingdom gross domestic product (at 1985 prices), 1955.1–1988.4.

UKTotalConsumption

(column 10)

United Kingdom total consumption (at 1985 prices), 1955.1–1988.4.

UKNondurablesConsumption

(column 11)

United Kindom nondurables consumption (at 1985 prices), 1955.1–1988.4.

UKExport

(column 12)

United Kindom exports of goods and services (at 1985 prices), 1955.1–1988.4.

UKImport

(column 13)

United Kindom imports of goods and services (at 1985 prices), 1955.1–1988.4.

UKPublicInvestment

(column 14)

United Kindom public investment (at 1985 prices), 1962.1–1988.4.

UKWorkforce

(column 15)

United Kindom workforce (consisting of workforce in employment and unemployment), 1955.1–1988.4.

SwedenNondurablesConsumption

(column 16)

Real per capita non-durables consumption in Sweden (measured in logs), 1963.1–1988.1.

SwedenDisposableIncome

(column 17)

Real per capita disposable income in Sweden (measured in logs), 1963.1–1988.1.

SA_SwedenNondurablesConsumption

(column 18)

Seasonally adjusted SwedenNondurablesConsumption with Census X-11 method, 1964.1–1988.1. (Using the approximate linear Census X-11 filter given in Table 4.1, p. 52 in Franses (1996) and generating the forecasts and backcasts as described in Ooms (1994)).

SA_SwedenDisposableIncome

(column 19)

Seasonally adjusted SwedenDisposableIncome with Census X-11 method, 1964.1–1988.1. (Using the same method as above.)

More details on the individual time series are given by Franses (1996).

Note

Most of the time series in dataFranses1996 are available as separate datasets in package ‘partsm’. The numbers should be the same but note that, at the time of writing this, not all datasets there carry complete time information.

Source

The data were downloaded from ⁠http://people.few.eur.nl/franses/research/data/data1.txt⁠, but this link is now broken.

References

Franses PH (1996). Periodicity and Stochastic Trends In Economic Time Series. Oxford University Press Inc., New York.

Examples

data(dataFranses1996)
class(dataFranses1996)
colnames(dataFranses1996)
dim(dataFranses1996) # c(148, 19)
plot(dataFranses1996[ , 2:11])

tipi <- dataFranses1996[ , "USTotalIPI"]
plot(tipi)
## convert to PeriodicTS and remove NA's at the start and end
pctipi <- pcts(tipi)
pctipi <- window(pctipi, start = availStart(pctipi), end = availEnd(pctipi))
plot(pctipi)

## convert  the whole dataset to class "PeriodicMTS"
pcfr <- pcts(dataFranses1996)

colnames(pcfr)[2:3] #  "USTotalIPI" "CanadaUnemployment"

## subset as "PeriodicMTS"
pcfr2to3 <- pcfr[2:3]
plot(pcfr2to3)
## "[" "PeriodicMTS" even with length one arg.
pcfr2to2  <- pcfr[2]
pcfr2to2a <- pcfr["USTotalIPI"] # same

## use "[[" or $ to get "PeriodicTS"
pcfr2 <- pcfr[[2]]
pcfr2a <- pcfr[["USTotalIPI"]] # same
pcfr2b <- pcfr$USTotalIPI      # same
identical(pcfr2, pcfr2a) # TRUE
identical(pcfr2, pcfr2b) # TRUE

cycle(pcfr)
frequency(pcfr)

Replace methods for date in package pcts

Description

Replace methods for date in package pcts.

Methods

signature(x = "BasicCycle")
signature(x = "Cyclic")

An example PAR autocorrelation function

Description

ex1 is the autocorrelation function used in the reference as an example when the solution of the periodic Yule-Walker system gives an invalid PAR model. This can happen only if Lambert-Lacroix's condition on the PAR order is not satisfied, see pdSafeParOrder.

Format

A function of two arguments

Source

See pp. 429–430 of the reference.

References

Lambert-Lacroix S (2005). “ Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(6), pp. 423-435.

Examples

data(ex1f)
## compute the first few autocorrelations
pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt")
## Fir a PAR(0,2) model
res0p2 <- alg1(pc3[],c(0,2))
## model is invalid since a partial autocorrelation is larger than one:
res0p2$be
## Find a modified order:
pdSafeParOrder(c(0,2)) # PAR(1,2)
## now the parcor's are fine:
res1p2 <- alg1(pc3[],c(1,2))
res1p2$be

Get the coefficients of a periodic filter

Description

Get the coefficients of a periodic filter.

Details

filterCoef is a generic function to extract the coefficients of periodic filters. Argument convention can be used to force a particular convention for the signs. The description here is for the methods defined in this package.

If convention is missing, the coefficient matrix is returned as stored in the object. Otherwise, if convention is one of the strings "BJ", "--" or "-", the coefficients returned have the opposite sign of those in the auxilliary polynomial (Box-Jenkins' convention). If convention is one of "SP", "++" or "+", the coefficients are as in the auxilliary polynomial (convention used in signal processing).

Value

a matrix

Methods

signature(object = "PeriodicBJFilter", convention = "character")
signature(object = "PeriodicSPFilter", convention = "character")

Dummy title

Description

~~ Dummy description ~~

Methods

signature(object = "PeriodicBJFilter")
signature(object = "PeriodicSPFilter")

Dummy title

Description

~~ Dummy description ~~

Methods

signature(object = "PeriodicBJFilter")
signature(object = "PeriodicSPFilter")

Fit periodic time series models

Description

Generic function with methods for fitting periodic time series models.

Usage

fitPM( model, x, ...)

Arguments

x

the time series.

model

a periodic model, see Details.

...

further arguments to be passed on to individual methods.

Details

This is a generic function.

model provides the specification of the model. In particular, the class of model determines what model is fitted. Specific values of the parameters are generally ignored by non-iterative methods but some methods can handle more detailed specifications, see the individual methods.

Value

the fitted model, typically an object of class class(model)

Methods

signature(model = "ANY", x = "ANY")

This is the default method. It simply exits with an error message stating that fitPM does not have a method for the model specified by model.

signature(model = "numeric", x = "ANY")

Fits a PAR model to x. model should be a vector of non-negative integers giving the PAR order. The length of this vector is taken to be the number of seasons.

This is a convenience method. It constructs a PAR model and callls the method for model = "PeriodicArModel".

signature(model = "PeriodicArModel", x = "ANY")

Fits a PAR model.

signature(model = "mcSpec", x = "ANY")

Fits a periodic model according to the specification given by model.

Currently this method uses mC.ss to set up the optimisation environment and then calls one of the optimisation functions in that environment as specified by argument optim.method, see below.

Additional arguments may be specified to control the optimisation.

Argument init can be used to give initial values. It is passed on to mC.ss (and so has the format required by it).

optim.method is the name of an optimisation function in the environment returned by mC.ss. The default is optim.method = "minim", which is based on the standard R function optim. Alternatives are "minimBB" or "minimBBLU". All this needs to be documented but see mC.ss and xx.ss for details.

Further arguments are passed on to the optimisation method. A typical argument supported by most optimisation functions is control.

signature(model = "PiPeriodicArModel", x = "ANY")

Fits a periodically integrated PAR model using the parameters of model as initial values. Calls pclspiar to do the actual work.

signature(model = "SiPeriodicArModel", x = "ANY")

Fits a seasonally integrated PAR model.

signature(model = "PeriodicArModel", x = "PeriodicMTS")

signature(model = "PeriodicArModel", x = "PeriodicTS")

Author(s)

Georgi N. Boshnakov

References

(todo: to be completed properly later)

Hipel KW, McLeod AI (1994). Time series modelling of water resources and environmental systems, Developments in water science; 45. London; Amsterdam: Elsevier.

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Examples

## newm1 <- list(phi = matrix(1:12, nrow=4), p=rep(3,4), period=4, si2 = rep(1,4))
## new_pfm1 <- PeriodicFilterModel(newm1, intercept=0)

## generate some data;
set.seed(1234)
simts1 <- pcts(rnorm(1024), nseasons = 4)

fitPM(c(3,3,3,3), simts1)
fitPM(3, simts1)
## the fit on the underlying data is equivalent.
fitPM(c(3,3,3,3), as.numeric(simts1))

## equivalently, use a PAR(3,3,3,3) model for argument 'model'
## here the coefficients of pfm1 are ignored, since the estimation is linear.
pfm1 <- PeriodicArModel(matrix(1:12, nrow = 4), order = rep(3,4), sigma2 = 1)
pfm1
## these give same results as above
fitPM(pfm1, simts1)
fitPM(pfm1, as.numeric(simts1))

fitPM(c(1,1,1,1), simts1)
fitPM(c(3,2,2,1), simts1)
fitPM(c(3,2,2,2), simts1)

pdSafeParOrder(c(3,2,2,1))
pdSafeParOrder(rev(c(3,2,2,1)))

x <- arima.sim(list(ar = 0.9), n = 960)
pcx <- pcts(x, nseasons = 4)
mx <- matrix(x, nrow = 4)

##pc.acf(mx)
##pc.acf(mx, maxlag=10)
## TODO: avoid the warning when length ot the time series is not multiple
autocovariances(t(mx), maxlag = 6, nseasons = 4)
autocovariances(t(mx))

##It is an error to have more columns than rows.
## autocovariances(mx, maxlag = 6, nseasons = 4)
## autocovariances(mx)

num2pcpar(mx, c(1,1,1,1), period = 4)
num2pcpar(mx, c(3,3,3,3), period = 4)

sipfm1 <- new("SiPeriodicArModel", iorder = 1, siorder = 1, pcmodel = pfm1)
sipfm1
fitPM(sipfm1, mx)
pfm1


## experiments and testing
fit1    <- fitPM(c(3,3,3,3), simts1)
fit1_mf <- new("MultiFilter", coef = fit1@ar@coef)
vs      <- mcompanion::mf_VSform(fit1_mf, form = "I")
tmp <- mcompanion::VAR2pcfilter(vs$Phi[ , -4],
                                Phi0inv = vs$Phi0inv, D = fit1@sigma2, what = "")
names(tmp) #  "pcfilter" "var"      "Uform"   
tmp$var
zapsmall(tmp$pcfilter)
fit1@ar@coef
all.equal(tmp$pcfilter[ , 1:3], fit1@ar@coef, check.attributes = FALSE) # TRUE
tmp$Uform
fit1@sigma2

## both give the matrix Sigma for the "I" form
identical(
    vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv)
    ,
    tmp$Uform$U0inv %*% diag(tmp$Uform$Sigma)  %*% t(tmp$Uform$U0inv)
) # TRUE

## no, this is a different matrix
var1_mat <- cbind(vs$Phi0, # identity matrix
                  - vs$Phi) # drop trailing zero columns?
var1_mat <- mcompanion::mCompanion(var1_mat)
var1_Sigma <- vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv)
abs(eigen(diag(nrow(var1_mat)) - var1_mat)$values)

Fit a subset trigonometric PAR model

Description

Fit a subset PAR model with trigonometric parameterisation.

Usage

fit_trigPAR_optim(x, order, nseasons, seasonof1st = 1, maxiter = 200, 
                  harmonics = NULL, sintercept = FALSE, tol = 1e-07, 
                  type = c("vecbyrow", "bylag"), verbose = TRUE)

Arguments

x

time series.

order

order, an integer number.

nseasons

number of seasons, an integer number.

seasonof1st

season of the first observation.

maxiter

max number of iterations.

harmonics

the harmonics to include in the model, vector of non-negative integers.

sintercept

if TRUE include seasonal intercept.

tol

when to stop the iterations.

type

type of parameterisation, currently one of "vecbyrow" or "bylag".

verbose

if TRUE print more details during estimation.

Details

Fits a subset PAR model using trigonometric parameterisation, i.e. Fourier series for the periodic coefficients written in terms of sines and cosines.

If argument type is bylag, the parameters for each lag are parameterised independently from other lags. If sintercept is TRUE, it has its own trigonometric representation.

If argument type is vecbyrow (“Vec operation by row”), the PAR parameters are stacked in a vector with all parameters for the first season, followed by all parameters for the second, and so on. The trigonometric parameterisation for this vector is used. So the fundamental frequency is 1/(nseasons * order). If sintercept is TRUE when type = vecbyrow, then then the intercept for eaach season is put before the PAR parameters and the fundamental frequency becomes 1/(nseasons * (order + 1). Putting together the intercepts and the PAR parameters may not be very useful for parsimonious trigonometric parameterisation, so to have a separate set of coefficients for the intercepts set attribute "merge" of sintercept to FALSE.

Value

an object from class SubsetPM

Note

This function may change.

Author(s)

Georgi N. Boshnakov

Examples

## see examples for class "SubsetPM"

Data for four stocks since 2016-01-01

Description

Data for four stocks since 2016-01-01.

Usage

data("four_stocks_since2016_01_01")

Format

A list with components "DELL","MSFT", "INTC", "IBM". Each component is a time series from class "xts" "zoo".

Details

Stock market data for Dell, Microsoft, Intel and IBM, from 2016-01-01 to 2020-04-17. The Dell data start from 2016-08-17. All data were downloaded from Yahoo Finance on 2020-04-18.

Source

https://finance.yahoo.com/

Examples

data(four_stocks_since2016_01_01)
DELL <- four_stocks_since2016_01_01$DELL
head(DELL)
tail(DELL)

dell <- pcts(DELL)

head(as_datetime(dell))
head(Pctime(dell))

## Weekends are totally absent from the data,
## so a Monday-Friday sub-cycle is created:
nSeasons(dell)
dell@cycle


## there are some NA's in the data, due to Bank holidays
Pctime(c(2624, 5), pcCycle(dell))               # "W2624 Fri"
as_datetime(Pctime(c(2624, 5), pcCycle(dell)))  # "2020-04-10 UTC"

## dell["2020-04-10 UTC"]

head(cycle(dell))

tail(Pctime(dell))
tail(as.Date(Pctime(dell)))

Methods for function head() in package pcts

Description

Methods for function head() in package pcts.

Methods

signature(x = "PeriodicTimeSeries")

Create environment for mc-fitting

Description

Creates an environment for mc-fitting. These functions are transitory, hence the strange names.

Usage

mC.ss(spec, ...)

xx.ss(period, type.eigval, n.root, eigabs, eigsign, co_r, co_arg, 
      init = NULL, len.block = NULL, mo.col, generators = NULL)

Arguments

spec

a model, an object of class mcSpec.

...

further arguments to be passed on to xx.ss.

period

the number of seasons.

type.eigval

types of the eigenvalues, a character vector with elements "r" or "cp", see Details.

n.root

number of roots. Currently the dimension of the matrix is set to this.

eigabs

The absolute values/moduli of the eigenvalues, numeric vector.

eigsign

The signs/moduli of the eigenvalues.

co_r

similar to eigabs but for the co parameters.

co_arg

similar to eigsign but for the co parameters.

init

initial values, see Details.

len.block

lengths of Jordan blocks.

mo.col

last non-zero column in the top of the matrix.

generators

~~ TODO: describe this argument. ~~

Details

mC.ss takes the specification of the model as an object of class mcSpec and calls xx.ss.

Basically, the value returned by these functions is an extended model specification together with an environment which can be used for fitting the model, exploring the results and trying various things. This may be used for getting better understanding of the model and the optimisation routines.

The result of both functions is a list, containing several functions and an environment. The environment (element env) is the most important element since it allows access to everything in the model environment. The function elements of the list are simply a convenience.

Several functions in env are available for fitting the model. Currently these are minim, minimBB and minimBBlu. The first argument of all these functions is a time series to which the model is to be fitted. By default, a conditional likelihood is being optimised. To base the optimisation on conditional sum of squares, set argument CONDLIK to FALSE. The remaining arguments in a call to any of the above functions are passed on to the corresponding optimisation routine (whose help page should be consulted for details).

minim uses the core R function optim. minimBB and minimBBlu use BBoptim from package BB. They result is a list, as returned by the corresponding optimisation function with the optimal parameters in element par. The elements of this vector are named to help somewhat in its interpretation but complete information about the fitted model can be obtained from the environment.

Firstly, at the end of the optimisation, the optimal parameters and other information are stored in env. If the same call (maybe with modified instructions for the optimisation) is repeated, these parameters will be used as initial values for a new optimisation run. This may be useful, for example, if the previous run didn't converge.

Secondly, properties of the fitted model and more useful representations can be obtained using functions in the environment or the convinience functions in the list returned by xx.ss.

optparam2mcparam converts a vector of parameters into the more familiar filter representation, where the i-th row contains the coefficients for the i-th season. This function takes one argument the vector of parameters, e.g. the one returned by the fitting functions. It updates a number of variables in env, computes the filter representation of the model and stores it in wrkmodel. It returns NULL. This function may be used for exploratory purposes or to set new values for the parameters, e.g. to be used as starting values for a new optimisation run.

mcparam2optparam does the opposite. It converts the current model in env to a vector of parameter. This function does not have arguments.

mclik computes the value of the conditional likelihood for given parameters. Its first argument is a time series, the second is a vector of parameters and the third is a vector of innovations. Only the first argument is compulsory. If param is not supplied, the current parameters in env are used. Otherwise, they are updated with the new parameters and then used. The innovations default to the zero vector. mcss is similar but computes the conditional sum of squares.

Argument init can be used to provide initial values. If it is missing or NULL, random initial values are generated for the free parameters. init may also be a numeric vector suitable for the call optparam2mcparam(init), see above. This vector would typically come from a previous optimisation run.

init may also be a list with elements "eigabs", "eigsign", "co_r", "co_abs". These components have the same meaning as the corresponding arguments of xx.ss.

TODO: more is needed here!

Value

A list with the following components:

fmcss

a function to compute the sum of squares for a model.

fparamvec

a function to convert mc-parameters to optimisation parameters.

fmcparam

a function to convert optimisation parameters to mc-parameters.

env

an object of class environment

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Examples

# test0 roots
spec.coz2 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(2,4))
spec.coz2
xxcoz2a <- mC.ss(spec.coz2)

## test0 roots
spec.coz4 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(3,4))
xxcoz4a <- mC.ss(spec.coz4)

Methods for function maxLag() in package 'pcts'

Description

Methods for function maxLag() in package 'pcts'.

Methods

signature(object = "PeriodicArmaFilter")

Examples

## non-periodic autocovariances
maxLag(autocovariances(AirPassengers))

## periodic
pcts_exdata() # creates ap, ap7to9, pcfr, pcfr2to4,

maxLag(autocovariances(ap, maxlag = 6))

## pcarma filter
m <- rbind(c(0.81, 0), c(0.4972376, 0.4972376))
ar_filt3 <- new("PeriodicBJFilter",  coef =  m, order = c(1,2))
arma_filt3 <- new("PeriodicArmaFilter", ar = ar_filt3)
maxLag(arma_filt3)

Class mcOptimCore

Description

Class mcOptimCore.

Extends

All reference classes extend and inherit methods from "envRefClass".

Fields

flag.exploring:: Object of class logical ~~
private.counter.fn:: Object of class integer ~~
period:: Object of class integer ~~
len.block:: Object of class integer ~~
n_col:: Object of class integer ~~
r_col:: Object of class integer ~~
cp_col:: Object of class integer ~~
ind.r.eigval:: Object of class integer ~~
r_ind:: Object of class integer ~~
ind.cp.eigval:: Object of class integer ~~
cp_ind:: Object of class integer ~~
filter.order:: Object of class integer ~~
ev_abs:: Object of class matrix ~~
ev_sign:: Object of class matrix ~~
co_r:: Object of class matrix ~~
co_arg:: Object of class matrix ~~
flag.generators:: Object of class logical ~~
par.ind:: Object of class ANY ~~
auto.ind:: Object of class ANY ~~
inf.ind:: Object of class ANY ~~
universe:: Object of class ANY ~~
col.minusinf.ind:: Object of class ANY ~~
col.inf.ind:: Object of class ANY ~~
ind1:: Object of class integer ~~
ind2:: Object of class integer ~~
ind3:: Object of class integer ~~
ind4:: Object of class integer ~~
n1:: Object of class integer ~~
n2:: Object of class integer ~~
n3:: Object of class integer ~~
n4:: Object of class integer ~~
seqn1:: Object of class integer ~~
seqn2:: Object of class integer ~~
seqn3:: Object of class integer ~~
seqn4:: Object of class integer ~~
co:: Object of class matrix ~~
initmodel:: Object of class ANY ~~
wrkmodel:: Object of class ANY ~~
model:: Object of class list ~~
tempnam:: Object of class ANY ~~
param_names:: Object of class character ~~
lo_bound:: Object of class ANY ~~
up_bound:: Object of class ANY ~~
mcss.cnt:: Object of class integer ~~
wrkev:: Object of class ANY ~~

Methods

mclik(param, x, eps):: ~~
minimBBlu(x, ..., CONDLIK):: ~~
mcss(param, x, eps):: ~~
matepshat(param, x, eps):: ~~
process.mcss.cnt(mclik, mepshat):: ~~
sigma2hat(param, x, eps):: ~~
initialize(...):: ~~
mcparam2optparam():: ~~
optparam2mcparam(param):: ~~
minimBB(x, ..., CONDLIK):: ~~
optimize(optimfn, mcmethod, x, ..., MCBOUNDS):: ~~
mcsigma2(param, x, eps):: ~~
minim(x, ..., CONDLIK):: ~~

Examples

showClass("mcOptimCore")

Asymptotic covariance matrix of periodic mean

Description

Asymptotic covariance matrix of periodic mean.

Usage

meanvarcheck(parmodel, n)

meancovmat(parmodel, n, cor = FALSE, result = "var")

Arguments

parmodel

a periodic model.

n

number of observations (TODO: need clarification here).

cor

if TRUE, return correlations

result

if "var", return the diagonal of the covariance matrix, otherwise return the matrix.

Details

Computes asymptotic covariance or correlation matrix of the periodic means.

Value

if result = "var" a matrix, otherwise a vector

Author(s)

Georgi N. Boshnakov

Examples

x <- arima.sim(list(ar=0.9), n=1000)
proba1 <- fitPM(c(3,2,2,2), x)

meancovmat(proba1, 100)
meancovmat(proba1, 100, cor = TRUE)
meancovmat(proba1, 100, result = "")
meancovmat(proba1, 100, cor = TRUE, result = "")

meanvarcheck(proba1, 100)

Get the cycle of a periodic object

Description

Get the cycle of a periodic object, a generic function.

Usage

modelCycle(object)

modelCycle(object, ... ) <- value

Arguments

object

an object.

value

the new value for the cycle, an object inheriting from "BasicCycle".

...

not used.

Details

modelCycle is essentially internal, for programming. The user level function to get the cycle of an object is pcCycle.

modelCycle returns the Cycle object (in the sense of package pcts), associated with object. modelCycle is a generic function which makes it possible to associate a cycle with objects from a class, without inheriting from the cycle classes.

By definition, NULL represents the model cycle of objects from classes with no (inherited) method for modelCycle.

The default method of modelCycle returns NULL. The default method for its replacement version throws error.

Value

for modelCycle, an object inheriting from class "BasicCycle" or NULL;

"modelCycle<-" is used for the side effect of changing the cycle of object.

Methods

signature(object = "ANY")
signature(object = "ModelCycleSpec")

Basic information about periodic ts objects

Description

Basic information about periodic periodic time series objects.

Usage

nCycles(x, ...)

nTicks(x)

nVariables(x, ...)

nSeasons(object)

Arguments

x, object

an object from a periodic time series class.

...

further arguments for methods.

Details

nTicks gives the number of time points, i.e. number of rows in the matrix representation.

nVariables gives the number of variables in the time series.

nSeasons gives the number of seasons of time series and other periodic objects.

nCycles gives the number of cycles available in the data, e.g. number of years for monthly data. It always gives an integer number. Currently, if the result is not an integer an error is raised. TODO: There is a case to round up or give the number of full cycles available but this seems somewhat dangerous if done quietly. A good alternative is to provide argument for control of this.

There are further functions to get or set the names of the units of season and the seasons, see allSeasons.

Value

an integer number

Author(s)

Georgi N. Boshnakov

Examples

ap <- pcts(AirPassengers)
nVariables(ap)
nTicks(ap)
nCycles(ap)
nSeasons(ap)

monthplot(ap)
boxplot(ap)

Number of seasons of a periodic object

Description

Number of seasons of a periodic object.

Usage

## S4 method for signature 'Cyclic'
nSeasons(object)

## same signature for all periodic classes in package "pcts"

Arguments

object

an object for which the notion of number of seasons makes sense.

Details

nSeasons is a generic function. This page gives is for the methods defined in package "pcts" - all periodic classes have (or inherit) a method.

Value

an integer number

Methods

signature(object = "DayWeekCycle")
signature(object = "MonthYearCycle")
signature(object = "PeriodicIntegratedArmaSpec")
signature(object = "QuarterYearCycle")
signature(object = "PeriodicMonicFilterSpec")
signature(object = "PeriodicInterceptSpec")
signature(object = "Cyclic")
signature(object = "BareCycle")
signature(object = "OpenCloseCycle")
signature(object = "Every30MinutesCycle")
signature(object = "PartialCycle")
signature(object = "VirtualPeriodicModel")
signature(object = "SarimaFilter")
signature(object = "VirtualArmaFilter")

Author(s)

Georgi N. Boshnakov

Examples

## scalar time series
ap <- pcts(AirPassengers)
nSeasons(ap) # 12

## multivariate time series
pcfr <- pcts(dataFranses1996)
nSeasons(pcfr) # 4

## five-day-week period
five_day_week <- BuiltinCycle(5)
five_day_week
nSeasons(five_day_week)

Number of observations in a time series

Description

Number of observations in a time series.

Methods

signature(x = "matrix")
signature(x = "numeric")
signature(x = "PeriodicTimeSeries")
signature(x = "Cyclic")

Fit PAR model using sample autocorrelations

Description

Fit PAR model using sample autocorrelations.

Usage

num2pcpar(x, order, result = NULL, ...)

Arguments

x

time series, a numeric vector.

order

PAR order, a single number or a vector with one entry for each season.

result

what to return, the default is to return the full model, see Details.

...

passed on to calc_peracf.

Details

Computes the periodic autocorrelations and fits a PAR model using the Periodic Levinson-Durbin algorithm.

The order is a vector of non-negative integers, specifying the autoregressive orders for each season. If order is a single number, then all seasons have that order.

mean controls centering in the computation of the autocorrelations. If mean is numeric, then subtract the supplied mean before computing the autocovariances. If mean is TRUE, the default, compute and subtract the sample periodic mean before computing the autocovariances. If mean is FALSE, do not centre the series, i.e. assume that the mean is zero.

If result is NULL, the default, returns the full model. If result = "coef", returns the PAR coefficients only (currently any value of result other than NULL has this effect).

Value

The coefficients of the fitted model or a list with components:

mean

the mean, set as described in Details.

coef

forward prediction coefficients.

scale

standard deviations of the innovations.

Author(s)

Georgi N. Boshnakov

Examples

## Not run: 
simts1 <- matrix(rnorm(100), nrow = 4)

num2pcpar(simts1, order = c(3,2,2,2), period = 4 )
num2pcpar(simts1, order = c(3,2,1,2), period = 4 )
pdSafeParOrder(c(3,2,1,2))
pdSafeParOrder(c(3,2,2,1))
num2pcpar(simts1, order = c(3,2,2,1), period = 4 )
num2pcpar(simts1, order = pdSafeParOrder(c(3,2,2,1)), period = 4 )

num2pcpar(simts1, order = c(3,2,1,2), period = 4 )
num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = rep(0,4) )
num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE )
num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE )$coef@m -
       num2pcpar(simts1, order = c(3,2,1,2), period = 4 )$coef@m

## End(Not run)

Compute asymptotic covariance matrix for PAR model

Description

Compute asymptotic covariance matrix for PAR model

Usage

parcovmatlist(parmodel, n, cor = FALSE, result = "list")

Arguments

parmodel

PAR model, object of class parModel

n

length of the series or a vector with one element for each season.

cor

If TRUE return correlation matrix.

result

if "list", the default, return a list, if "Matrix" return a Matrix object, otherwise return an ordinary matrix, see Details.

Details

Uses eq. (3.3) in the reference.

If result = "list", parcovmatlist returns a list whose s-th element is the covariance matrix of the PAR parameters for the s-th season. Otherwise, if result = "Matrix" it returns a block-diagonal matrix created by .bdiag() from package "Matrix". If result = "matrix" it returns an ordinary matrix (with the current implementation this is returned for any value other than "list" or "Matriix").

Value

a list, matrix or block-diagonal matrix, as described in Details

Author(s)

Georgi N. Boshnakov

References

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.

Examples

x <- arima.sim(list(ar=0.9), n=1000)
proba1 <- fitPM(c(3,2,2,2), x)

parcovmatlist(proba1, 100)
parcovmatlist(proba1, 100, cor = TRUE)
sqrt(diag(parcovmatlist(proba1, 100, cor = TRUE)[[1]]))

meanvarcheck(proba1, 100)

Compute periodic partial autocorrelations

Description

Methods for computation of periodic partial autocorrelations.

Methods

signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")
signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "ANY")

Compute periodic partial autocovariances

Description

Compute periodic partial autocovariances.

Methods

signature(x = "VirtualPeriodicAutocovariances")

Compute periodic partial coefficients

Description

Methods for computation of periodic partial coefficients.

Methods

signature(x = "PeriodicArModel")
signature(x = "VirtualPeriodicAutocovariances")

Compute periodic partial variances

Description

Compute periodic partial variances.

Methods

signature(x = "VirtualPeriodicAutocovariances")

Applies a periodic ARMA filter to a time series

Description

Filter time series with a periodic arma filter. If whiten is FALSE (default) the function applies the given ARMA filter to eps (eps is often periodic white noise). If whiten is TRUE the function applies the “inverse filter” to x, effectively computing residuals.

Usage

pc.filter(model, x, eps, seasonof1st = 1, from = NA, whiten = FALSE,
          nmean = NULL, nintercept = NULL)

Arguments

x

the time series to be filtered, a vector.

eps

residuals, a vector or NULL.

model

the model parameters, a list with components "phi", "theta", "p", "q", "period", "mean" and "intercept", see Details.

seasonof1st

the season of the first observation (i.e., of x[1]).

from

the index from which to start filtering.

whiten

if TRUE use x as input and apply the inverse filter to produce eps ("whiten" x), if FALSE use eps as input and generate x ("colour" eps).

nmean

a vector of means having the length of the series, see Details.

nintercept

a vector of intercepts having the length of the series, see details.

Details

The model is specified by argument model, which is a list with the following components:

phi: the autoregression parameters,
theta: the moving average parameters,
p: the autoregression orders, a single number or a vector with one element for each season,
q: the moving average orders, a single number or a vector with one element for each season,
period: number of seasons in a cycle,
mean: means of the seasons,
intercept: intercepts of the seasons.

The relation between x and eps is assumed to be the following. Let

y_t = x_t - mu_t

be the mean corrected series, where mu_t is the mean, see below. The equation relating the mean corrected series, y_t=x_t - \mu_t, and eps is the following:

y_t = c_t + \sum_{i=1}^{p_t} \phi _t(i)y _{t-i} + \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} + \varepsilon_t

where c_t is the intercept, nintercept. The inverse filter is obtained by writing this as an equation expressing \varepsilon_t through the remaining quantities.

If whiten = TRUE, pc.filter uses the above formula to compute the filtered values of x for t=from,...,n, i.e. whitening the time series if eps is white noise. If whiten = FALSE, eps is computed, i.e. the inverse filter is applied x from eps, i.e. “colouring” x. In both cases the first few values in x and/or eps are used as initial values.

Essentially, the mean is subtracted from the series to obtain the mean-corrected series, say y. Then either y is filtered to obtain eps or the inverse filter is applied to obtain y from eps finally the mean is added back to y and the result returned.

The mean is formed by model$mean and argument nmean. If model$mean is supplied it is recycled periodically to the length of the series x and subtracted from x. If argument nmean is supplied, it is subtracted from x. If both model$mean and nmean are supplied their sum is subtracted from x.

The above gives a vector y, y_t=x_t - \mu_t, which is then filtered. If the mean is zero, y_t=x_t in the formulas below.

Finally, the mean is added back, x_t=y_t+\mu_t, and the new x is returned.

The above gives a vector y which is used in the filtering. If the mean is zero, y_t=x_t in the formulae below.

pc.filter can be used to simulate pc-arma series with the default value of whiten=FALSE. In this case eps is the input series and y the output.

y_t = c_t + \sum_{i=1}^{p_t} \phi _t(i)y _{t-i} + \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} + \varepsilon_t

Then model$mean or nmean are added to y to form the output vector x.

Residuals corresponding to a series y can be obtained by setting whiten=TRUE. In this case y is the input series. The elements of the output vector eps are calculated by the formula:

\varepsilon_t = - c_t - \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} - \sum_{i=1}^{p_t} \phi _t(i)y _{t-i} + y_t

There is no need in this case to restore x since eps is returned.

In both cases any necessary initial values are assumed to be already in the vectors. If from is not supplied it is chosen as the smallest i such that for all t\ge i, t-p[t]>0 and t-q[t]>0, i.e. the filter will not require negative indices for x or eps.

pc.filter calls the lower level function pc.filter.xarma to do the computation.

Value

The filtered series: the modified x if whiten=FALSE, the modified eps if whiten=TRUE.

Level

Author(s)

Georgi N. Boshnakov

Filter time series with periodic arma filters

Description

Filter time series with periodic arma filters with or options for periodic and non-periodic intercepts.

Usage

pc.filter.xarma(x, eps, phi, theta, period, p, q, n, from,
              seasonof1st = 1, intercept = NULL, nintercept = NULL)

Arguments

x

the time series to be filtered, a vector.

eps

the innovations, a vector.

phi

the autoregression parameters, a matrix.

theta

the moving average parameters, a matrix.

period

the period (number of seasons in a year).

p

the autoregression orders, recycled to period if length(p)=1.

q

the moving average orders, recycled to period if length(q)=1.

n

a positive integer, the time index of the last observation to be filtered.

from

a positive integer, the time index of the first observation to be filtered.

seasonof1st

a positive integer, the season of the time index of x[1], see Details.

intercept

the intercepts of the seasons, a vector of length period.

nintercept

intercepts, a vector of the same length as x.

Details

pc.filter.xarma is somewhat lower level. The user level function is pc.filter which uses pc.filter.xarma to do the computations.

pc.filter.xarma filters the time series x by the following formula (for t=from,...,n):

x_t = c_t + \sum_{i=1}^{p_t} \phi _t(i)x _{t-i} + \sum_{i=1}^{q_t} \theta_t(i)\varepsilon_{t-i} + \varepsilon_t,

where c_t is the overall intercept at time t, see below. Values of x[t] for t outside the range from,n, if any, are left unchanged. Values for t<from are used as initial values when needed.

Two intercepts are provided for convenience and some flexibility. The periodic intercept, intercept, is a vector of length period. It is replicated to length n, taking care to ensure that the first element of the resulting vector, say a, starts with intercept[seasonof1st]. nintercept can be an arbitrary vector of length n. It can be used to represent trend or contributions from covariates. nintercept is not necessarilly periodic and argument seasonof1st does not affect its use. The overall intercept is obtained as the sum c = a + nintercept.

Usually x is a numeric vector but it can also be a matrix in which each column represents the data for one “year”. Also, the length of x is typically, but not necessarilly, equal to n. It is prudent to ensure that length(x) >= n and this must be done if x is a matrix.

Argument phi is ignored if p==0, argument theta is ignored if q==0.

pc.filter.xarma is meant to be called by other functions whose task is to prepare the arguments with proper checks. It does not make much sense to repeat the checks in pc.filter.xarma. In particular, no check is made to ensure that from and n are correctly specified.

This is a low level function meant to be used with basic vectors and matrices. TODO: Implement in C/C++. In the current implementation. it accesses the elements of the arguments with straightforward indexing, so objects from classes may be used as well, provided that x[t], eps[t], phi[t,i], theta[t,i], as well as assignment to x[t], are defined for scalar indices.

Value

Returns x with x[from] to x[n] filled with the filtered values and values outside the interval from,...,n left unchanged.

The mode of x is left unchanged. In particular, x may be a matrix with each row representing the data for a season. This is convenient since periodic time series are often more easily processed in this form.

Level

0 (base)

Author(s)

Georgi N. Boshnakov

function to compute estimates of the h weights

Description

The h coefficients are scaled cross-covariances between the time series and the innovations. This function computes estimates for h using as input the observed series, a series of estimated innovations, and an estimate of the variance of the innovations.

Usage

pc.hat.h(x, eps, maxlag, si2hat)

Arguments

x

the observed time series x(t)

eps

a series of esimated innovations

maxlag

maximum lag

si2hat

estimate of the variance of the innovations

Details

If missing, the variance of the innovations is estimated from eps.

Value

A matrix of the coefficient up to lag maxlag with one row for each season.

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.

Compute periodic autocorrelations from PAR coefficients

Description

Compute periodic autocorrelations from PAR coefficients. This effectively solves the inverse problem to that solved by the periodic Levinson-Durbin algorithm but does not use a recursion.

Usage

pcAR2acf(coef, sigma2, p, maxlag = 10)

Arguments

coef

PAR coefficients, a matrix, see Details.

sigma2

innovations variances.

p

PAR order.

maxlag

How many lags to compute.

Details

coef is a matrix with the coefficients for season i in the i-th row. The coefficients start from lag 1.

The first few autocorrelations are computed by solving a linear system, see the references. The rest, are generated using the periodic Yule-Walker equations.

Value

a matrix, in which row s contains the acf's for season s for lags 0, 1, ..., maxlag (in this order).

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN, Boteva A (1992). “An algorithm for the computation of the theoretical autocovariances of a periodic autoregression process.” Varna.

Examples

m <- rbind( c(0.81, 0), c(0.4972376, 0.4972376) )
si2 <- PeriodicVector(c(0.3439000, 0.1049724))

pcAR2acf(m)
pcAR2acf(m, si2)
pcAR2acf(m, si2, 2)
pcAR2acf(m, si2, 2, maxlag = 10)


# same using pcarma_acvf_lazy directly
m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )

testphi <- slMatrix(init = m1)
myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 10)
myf(1:2, 0:9)    # get a matrix of values

all(myf(1:2, 0:9) == pcAR2acf(m, si2, 2, maxlag = 9)) # TRUE

Apply a function to each season

Description

Apply a function to each season.

Usage

pcApply(object, ...)

## S4 method for signature 'numeric'
pcApply(object, nseasons, FUN, ...)

## S4 method for signature 'matrix'
pcApply(object, nseasons, FUN, ...)

## S4 method for signature 'PeriodicTS'
pcApply(object, FUN, ...)

## S4 method for signature 'PeriodicMTS'
pcApply(object, FUN, ...)

Arguments

object

an object for which periodic mean makes sense.

nseasons

number of seasons.

FUN

a function, as for apply.

...

further arguments for FUN.

Details

For univariate periodic time series, pcApply applies FUN to the data for each season. For multivariate periodic time series, this is done for each variable.

The methods for "numeric" and "matrix" are equivalent to those for "PeriodicTS" and "PeriodicMTS", respectively. The difference is that the latter two don't need argument nseasons and take the names of the seasons from object.

Argument "..." is for further arguments to FUN. In particular, with many standard R functions argument na.rm = TRUE can be used to omit NA's, see the examples.

In the univariate case, when length(object) is an integer multiple of the number of seasons the periodic mean is equivalent to apply(matrix(object, nrow = nseasons), 1, FUN, ...).

Value

numeric or matrix for the methods described here, see section Details.

Methods

signature(object = "matrix")
signature(object = "numeric")
signature(object = "PeriodicMTS")
signature(object = "PeriodicTS")

Author(s)

Georgi N. Boshnakov

Examples

pcApply(pcts(presidents), mean, na.rm = TRUE)
pcMean(pcts(presidents), na.rm = TRUE) # same

pcApply(pcts(presidents), median, na.rm = TRUE)
pcApply(pcts(presidents), var, na.rm = TRUE)
pcApply(pcts(presidents), sd, na.rm = TRUE)

pcfr2to4 <- pcts(dataFranses1996)[2:4]
pcApply(pcfr2to4, median, na.rm = TRUE)
pcApply(pcfr2to4, sd, na.rm = TRUE)

Compute the sum of squares for a given PAR model

Description

Compute the sum of squares for a given PAR model.

Usage

pcAr.ss(x, model, eps = numeric(length(x)))

Arguments

x

time series, a numeric vector.

model

a model.

eps

residuals, defaults to a vector of zeroes. This may be used for models with moving average terms, for example.

Details

todo:

Value

a number

Author(s)

Georgi N. Boshnakov

Create or extract Cycle objects

Description

pcCycle() is a generic function with methods for creating, converting, modifying, and extracting cycle objects. BuiltinCycle() is a function to create cycle objects from the builtin cycle classes.

Usage

pcCycle(x, type, ...)

BuiltinCycle(n, coerce = FALSE, first = 1, stop = TRUE)

Arguments

x

an object, methods include numeric, character and cyclic objects, see Details.

type

class of the result. If equal to "auto", the default, the class is determined by the argument(s), otherwise should be the name of a cycle class.

...

further arguments for methods.

n

number of seasons, an integer.

coerce

if TRUE coerce the objects to a modifiable cycle class, currently "SimpleCycle".

first

which season is first for this object.

stop

if TRUE, the default, throw error if there is no builtin class with n seasons, otherwise create a "BareCycle" object.

Details

pcCycle serves as both a constructor and extractor of cycle objects. It is meant to just do the right thing, relieving the user from the burden of specifying a particular cycle class.

If x is numeric it constructs a cycle object with period x and additional properties as specified by the other arguments. If x is a character string, it is taken to be the name of one of the builtin cycles.

pcCycle can be used to create a modified version of a cycle object and/or convert it to another cycle type. This is done by providing a cycle object as argument x, i.e. one inheriting from "BasicCycle".

If x inherits from "Cyclic", pcCycle returns its cycle component.

Argument type should be rarely needed, except maybe to conveniently force conversion of the builtin type to an ordinary type.

The descriptions of the individual methods in section Methods give some further specific details.

BuiltinCycle is a convenience function to create objects from builtin cycle classes by specifying the number of seasons. The builtin cycle classes are esseintially fixed, except that which season is considered first can be changed using argument first. If other modifications are desired, convert the returned builtin cycle object to class "SimpleCycle". This can be done also in the call to BuiltinCycle() by specifying coerce = TRUE.

By default, BuiltinCycle throws an error if there is no builtin class with the requested number of seasons. Set argument stop to FALSE to create an object from class "BareCycle" instead (and it will be converted to "SimpleCycle" if coerce = TRUE). Argument stop is mainly for programming.

Value

for pcCycle, an object from one of the cycle classes;

for BuiltinCycle, an object from one of the builtin classes, coerced if requested.

Methods

signature(x = "numeric", type = "missing"): creates a cycle object with period x. If x is the only argument, a "BareCycle" object is created, otherwise the constructor of "SimpleCycle" is invoked with all arguments except type passed on to it.
signature(x = "character", type = "missing"): creates an object from the class specified by x. Currently this is equivalent to new(x, ...) but somewhat more portable. Future amendments may use a more suitable class for some combinations of the arguments. Also, if a class is renamed, a code will be inserted here to create an equivalent object.
signature(x = "numeric", type = "character")
signature(x = "character", type = "character"): first call the method with type = "missing", then convert the result to class type.
signature(x = "Cyclic", type = "ANY"): extracts the cycle component of x (x@cycle). Currently ignores the remaining arguments.
signature(x = "BasicCycle", type = "missing"): convert an object from any cycle class to class "SimpleCycle". This is like as(x, "SimpleCycle") but can have further arguments.
signature(x = "BasicCycle", type = "character"): convert an object from any cycle class to class type.
signature(x = "ts", type = "missing")
signature(x = "ts", type = "character"): when x is of class "ts", extract the frequency and convert it to a cycle class. Just as for "ts", certain frequencies are taken to correspond to specific classes. While base R treats periodicities 4 and 12 specially, pcCycle extends this to all builtin classes in pcts. Argument type can be used to overwrite this default behaviour by requesting a specific class. In particular, type = "BareCycle" and type = "" cause the result to be "BareCycle".
signature(x = "PeriodicTimeSeries", type = "missing")
signature(x = "PeriodicTimeSeries", type = "character"): extract the cycle part of an object inheriting from "PeriodicTimeSeries", currently "PeriodicTS" or "PeriodicMTS". Argument type can be used to force the result to be from a specific cycle class, as in the methods for "ts".

Author(s)

Georgi N. Boshnakov

Examples

## pcCycle
pcCycle(4)
pcCycle(4, seasons = c("Spring", "Summer", "Autumn", "Winter"))

pcCycle("QuarterYearCycle")
BuiltinCycle(4) # same, recommended

pcCycle("QuarterYearCycle", type = "BareCycle")
pcCycle("QuarterYearCycle", type = "SimpleCycle")

## BuiltinCycle
BuiltinCycle(2)  # "OpenCloseCycle"
BuiltinCycle(4)  # "QuarterYearCycle"
BuiltinCycle(5)  #  five day week cycle
BuiltinCycle(7)  # "DayWeekCycle"
BuiltinCycle(12) # "MonthYearCycle"
BuiltinCycle(48) # "Every30MinutesCycle"

## error, since there is no builtin cycle with 19 seasons:
## BuiltinCycle(19)

## use stop = FALSE to reate a default cycle in this case
BuiltinCycle(19, stop = FALSE)
BuiltinCycle(19, coerce = TRUE, stop = FALSE)

Compute periodic mean

Description

Compute periodic mean, generic function.

Usage

pcMean(object, ...)

## S4 method for signature 'numeric'
pcMean(object, nseasons, ...)

## S4 method for signature 'matrix'
pcMean(object, nseasons, ...)

## S4 method for signature 'PeriodicTS'
pcMean(object, ...)

## S4 method for signature 'PeriodicMTS'
pcMean(object, ...)

Arguments

object

an object for which periodic mean makes sense.

nseasons

number of seasons.

...

further arguments for methods.

Details

For univariate periodic time series, pcMean computes the mean for each season and returns a named vector. For multivariate periodic time series, the result is a matrix with one column for each variable.

Argument na.rm = TRUE can be used to omit NA's.

In the univariate case, when length(object) is an integer multiple of the number of seasons the periodic mean is equivalent to computing the row means of matrix(object, nrow = nseasons).

Value

numeric or matrix for the methods described here, see section ‘Details’.

Methods

signature(object = "matrix")
signature(object = "numeric")
signature(object = "PeriodicMTS")
signature(object = "PeriodicTS")
signature(object = "VirtualPeriodicArmaModel")

Author(s)

Georgi N. Boshnakov

Examples

pcMean(pcts(presidents))
pcMean(pcts(presidents), na.rm = TRUE)

pcMean(pcts(dataFranses1996)[2:5], na.rm = TRUE)

pcMean(1:20, nseasons = 4)
m <- matrix(1:20, nrow = 4)
all(apply(m, 1, mean) == pcMean(1:20, nseasons = 4)) # TRUE

Plot periodic time series

Description

Plot periodic time series.

Usage

## S3 method for class 'PeriodicTimeSeries'
boxplot(x, ...)

## S3 method for class 'PeriodicTimeSeries'
monthplot(x, ylab = deparse(substitute(x)), base, ...)

Arguments

x

a periodic time series object.

...

further arguments to be passed to the plotting function.

ylab

label for the y-axis, only used for univariate time series.

base

a function for use for computing reference lines.

Details

Functions for periodic/seasonal plots and boxplots.

Author(s)

Georgi N. Boshnakov

Examples

ap <- pcts(AirPassengers)
monthplot(ap)
boxplot(ap)

fr23 <- pcts(dataFranses1996[ , 2:3])
monthplot(fr23)
boxplot(fr23)

Test for periodicity

Description

Test for periodicity

Usage

pcTest(x, nullmodel, nseasons, ...)

Arguments

x

the object to be tested, e.g. a time series or a periodic acf

nullmodel

specification of the test to be performed

nseasons

number of seasons

...

additional arguments to be passed on to methods

Details

This is a generic function which acts as a dispatcher for various tests for periodicity and periodic correlation.

x is typically a time series but conceptually it is an object containing the statistics needed for carrying out the requested test. For example, x may be the periodic autocovariance function for tests based on sample autocorrelations and autocovariances.

The method with signature (x = "ANY", nullmodel = "character") may be considered as default for pcTest. The “real” default method simply prints an error message.

Value

a list containing the results of the requested test, see the individual methods for details

Methods

signature(x = "ANY", nullmodel = "character")

Argument nullmodel specifies the test to be performed. It should be a single character string. If it is one of the strings recognised by this method, the test specified below is carried out. Otherwise nullmodel is taken to be the name of a function which is called with arguments (x,...).

Currently, the following character strings are recognised:

"wn": Box test for (non-periodic) white noise, simply calls Box.test.
"piar": Franses (1996) test for periodic integration.

signature(x = "slMatrix", nullmodel = "character")

x here is the periodic autocovariance function. This method works similarly to the method for signature (x = "ANY", nullmodel = "character"), see its description.

Currently, the following character strings are recognised:

"pwn": Ljung-Box test for periodic white noise,
"periodicity": McLeod test for periodic correlation.

signature(x = "numeric", nullmodel = "character")

signature(x = "PeriodicTimeSeries", nullmodel = "character")

Note

TODO: critical values

Author(s)

Georgi N. Boshnakov

Examples

cu <- pcts(dataFranses1996[ , "CanadaUnemployment"])
cu <- window(cu, start = availStart(cu), end = availEnd(cu))

test_piar(cu, 4, 1, sintercept = TRUE)
pcTest(cu, "piar", 4, 1, sintercept = TRUE)

Compute normalising factors

Description

Compute a matrix of factors such that elementwise division of the periodic autocovariance matrix by it will give the periodic autocorrelations.

Usage

pc_sdfactor(sd, maxlag)

Arguments

sd

standard deviations of the seasons numeric.

maxlag

maximal lag, a number.

Value

a matrix of coefficients of size period x (maxlag+1). The length of sd is taken to be the period.

Author(s)

Georgi N. Boshnakov

Examples

## equivalent to  data(Fraser, package = "pear")
Fraser <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12))

logfraser <- window(pcts(log(Fraser)), start = c(1913, 1))
acvf1 <- autocovariances(logfraser, maxlag = 2)
fac <- pc_sdfactor(sqrt(acvf1[ , 0]), 2)
fac[ , 1:3]

acrf1 <- autocorrelations(logfraser, maxlag = 2)
all.equal(acvf1[], acrf1[] * fac) # TRUE

Compute PAR autocovariance matrix

Description

Compute PAR autocovariance matrix

Usage

pc.acf.parModel(parmodel, maxlag = NULL)

pcacfMat(parmodel)

Arguments

parmodel

PAR model, an object of class parModel.

maxlag

maximum lag

Details

pc.acf.parModel returns the autocovariances of a PAR model in season-lag form with maximum lag equal to maxlag. If maxlag is larger than the available precomputed autocovariances, they missing ones are computed using the Yule-Walker relations. Note that pc.acf.parModel assumes that there are enough precomputed autocovariances to use the Yule-Walker recursions directly.

TODO: pc.acf.parModel is tied to the old classes since it accesses their slots. Could be used as a template to streamline the method for autocovariances for class "PeriodicAutocovariance".

The season-lag form can be easily converted to other forms with the powerful indexing operator, see the examples and slMatrix-class.

pcacfMat is a convenience function for statistical inference. It creates a covariance matrix with dimension chosen automatically. This covariance matrix is such that the asymptotic covariance matrix of the estimated parameters can be obtained by dividing sub-blocks by innovation variances and inverting them. See, eq. (3.3) in the reference.

Value

for pcacfMat, a matrix

for pc.acf.parModel, an slMatrix

Author(s)

Georgi N. Boshnakov

References

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.

Examples

x <- arima.sim(list(ar = 0.9), n = 1000)
proba1 <- fitPM(c(3,2,2,2), x)

acfb <- pc.acf.parModel(proba1, maxlag = 8)
acfb[4:(-2), 4:(-2), type = "tt"]

pcacfMat(proba1)

Variances of sample periodic autocorrelations

Description

Computes the variances of sample periodic autocorrelations from periodic white noise.

Usage

pcacf_pwn_var(nepoch, period, lag, season)

Arguments

lag

desired lags, a vector of positive integers.

season

desired seasons.

nepoch

number of epochs.

period

number of seasons.

Details

These are given by McLeod (1994), see the reference, eq. (4.3).

Value

A matrix whose (i,j)th entry contains the variance of the autocorrelation coefficient for season season[i] and lag lag[j].

Author(s)

Georgi N. Boshnakov

References

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.

Examples

pcacf_pwn_var(79, 12, 0:16, 1:12)

Periodic Levinson-Durbin algorithm

Description

Calculate partial periodic autocorrelations, forward and backward prediction coefficients and error variances using the periodic Levinson-Durbin algorithm.

Usage

alg1(r, p)

Arguments

r

periodic autocovariances, a matrix, see ‘Details’.

p

autoregressive orders, numeric vector.

Details

alg1(r,p) calculates the partial periodic correlations from autocovariances r and autoregression orders p. The matrix r has the same format as that of the r slot of pcAcvf objects. The periodicity, d, is set equal to the number of rows in r. If the length of p is not equal to the periodicity, all autoregressive orders are set to the first element of p. This last feature is really meant to be used only with a scalar p.

The convention for the signs of the coefficients is the one from Boshnakov(1996) and is consistent with other R time series functions.

pmax below stands for the maximal element of p, i.e. the maximal AR order.

As in the non-periodic case, the periodic Levinson-Durbin algorithm fits recursively models of order 0, 1, ..., pmax. Namely, at step i the AR orders for all seasons are set to i. This is done in a way that correctly handles the case when not all elements of p are equal, see the references.

The essential quantities calculated by the periodic Levinson-Durbin algorithm are returned as matrices, whose ith rows contain values for season i. The complete details depend on the quantities, as described below.

The partial autocorrelations, the forward innovation variances and the backward innovation variances are returned as matrices with d rows and 1+pmax columns, whose j-th columns contain the quantities for order j-1 (partial autocorrelations, forward innovation variances and backward innovation variances, respectively). Note that the lag-0 partial autocorrelations are the autocovariances for lag 0, see the references for details.

The forward autoregression parameters are returned as a list whose jth element is a matrix containing the coefficients for order j. Similarly for the backward autoregression parameters.

One often is interested in the model of order p only. Its coefficients are given by af[[pmax]], while the innovation variances are in the last column of fv.

Value

A list with the following elements.

orders

autoregression orders

be

partial autocorrelations, a matrix with d rows

fv

forward innovation variances, a matrix with d rows

bv

backward innovation variances, a matrix with d rows

af

forward autoregression parameters, a list with one element for the parameters for each order.

ab

backward autoregression parameters, a list with one element for the parameters for each order.

Note

The autoregression orders of the output are not necessarilly the same as those specified in the call. There may be no PAR model with the requested orders, see the references.

Author(s)

Georgi N. Boshnakov

References

Lambert-Lacroix S (2000). “On periodic autoregressive process estimation.” IEEE Transactions on Signal Processing, 48(6), 1800-1803.

Lambert-Lacroix S (2005). “Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(3), 423-435.

Examples

r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900))
alg1(r1,2)

## pc2 <- pcAcvf(init=r1)
## pc2a <- pcAcvf(init=r1,seasonnames=c("am","pm"), periodunit="day")

# example of Lambert-Lacroix
data(ex1f)
pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt")
res0p2 <- alg1(pc3[],c(0,2))
res1p2 <- alg1(pc3[],c(1,2))
res3p3 <- alg1(pc3[],c(3,3))

paramsys1 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2)
t1 <- solve(paramsys1$A,paramsys1$b)

# this is from tests.r but I have lost t1
# set it to pc3 below
# note: t1 is not the t1 computed above and in other examples!

t1 <- pc3
t1
t1[]
alg1(t1[],c(1,1))
alg1(t1[],c(1,0))
alg1(t1[],c(0,1))
alg1(t1[],c(5,5))
alg1(t1[],c(2,2))
alg1(t1[],c(2,3))
alg1(t1[],c(3,3))
alg1(t1[],c(4,4))
alg1(t1[],c(5,5))

Give partial periodic autocorrelations or other partial prediction quantities for a pcAcvf object.

Description

Give partial periodic autocorrelations or other partial prediction quantities for a pcAcvf object.

Usage

alg1util(x, s, at0 = 1)

Arguments

x

an object of a class inheriting from pc.Model.WeaklyStat

s

the required quantity, the name of one of the elements of the list returned by alg1.

at0

if not identical to "var", replace the elements of the result at lag zero with 1, see ‘Details’.

Details

This function is a wrapper for alg1(). It calls alg1, to do the computations and returns the requested element as an object from class slMatrix. The model order is set to the maximal lag avialable in x,

If at0 is the character string "var", then the lag zero values in the result are set to the lag zero autocovariances, otherwise they are set to 1. This is mainly relevant for the periodic partial autocorrelations (s="be"), since the setting at0="var" ensures that they are in one to one correspondence with the autocovariances.

Value

the requested quantity as an object of type slMatrix

Author(s)

Georgi N. Boshnakov

References

Lambert-Lacroix S (2000). “On periodic autoregressive process estimation .” IEEE Transactions on Signal Processing, 48( 6 ), pp. 1800-1803.

Lambert-Lacroix S (2005). “ Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(6), pp. 423-435.

Examples

r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900))

# example of Lambert-Lacroix
data(ex1f)
pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt")
res0p2 <- alg1(pc3[],c(0,2))
res1p2 <- alg1(pc3[],c(1,2))
res3p3 <- alg1(pc3[],c(3,3))

Fit a PC-ARMA model to a periodic autocovariance function

Description

Fit a PC-ARMA model to a periodic autocovariance function.

Usage

pcarma_acvf2model(acf, model, maxlag)

Arguments

acf

a periodic autocovariance function, an object of class pcAcvf.

model

a pc- arma model, an object of class pcARMApq. (todo: check!)

maxlag

not used. (todo: check!)

Value

~Describe the value returned If it is a LIST, use

comp1

Description of 'comp1'

comp2

Description of 'comp2'

...

Author(s)

Georgi N. Boshnakov

References

Examples

data(ex1f)
pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt")
# pcarma_param_system(pc3, NULL, NULL, 2, 0, 2)
parsys <- pcarma_param_system(pc3, NULL, NULL, c(2,2), 0, 2)
param <- solve(parsys$A,parsys$b)

# res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0,period=2))
# res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0))
# res <- pcarma_acvf2model(pc3, list(p=c(1,2),period=2))
res <- pcarma_acvf2model(pc3, list(p=c(1,2)))

print(param)
print(res)

Functions to compute various characteristics of a PCARMA model

Description

Given a PCARMA model, create a function for computing autocovariances or coefficients of the corresponding infinite moving average representation or prepare the linear system whose solution provides the first few autocovariances of the model.

Usage

pcarma_acvf_lazy(phi, theta, sigma2, p, q, period, maxlag = 100)
pcarma_h_lazy(phi, theta, p, q, period, maxlag = 200)
pcarma_acvf_system(phi, theta, sigma2, p, q, period)
pcarma_param_system(acf, h, sigma2, p, q, period)
pcarma_h(h, na = NA)

Arguments

phi

the autoregression parameters, an object of class "slMatrix"

theta

the moving average parameters, an object of class "slMatrix"

sigma2

the innovation variances, an object of class "PeriodicVector" or a vector of size period, Details.

p

the (maximal) autoregression order or the autoregression orders.

q

the (maximal) moving average order or the moving average orders.

period

number of seasons in an epoch

maxlag

maximal lag for which the result is stored internally.

acf

the autocovariance function, an object of class pcAcvf, slMatrix, or similar

h

pcarma_param_system, h(t,k) is expected to return the coefficient h_{t,k}. h is usually created by pcarma_h_lazy. For pcarma_h, a matrix of h(t,i) coefficients.

na

not used currently, controls what to do for large lags.

Details

Compute acvf from parameters

pcarma_acvf_lazy creates a function that will compute (on demand) values of the acf by a recursive formula. Computed values are stored internally for lags up to maxlag.

System for acvf from parameters

pcarma_acvf_system forms a linear system for the calculation of autocovariances from the parameters of a pc-arma model. The argument theta is not used if q=0 and phi is not used if p=0.

System for parameters from acvf

pcarma_param_system takes the periodic autocovariances of a pc-arma model and computes a matrix and a vector representing the linear system whose solution provides the parameters of the model.

Scalar p specifies the same autoregression order for each season, similarly for q. p and q may be vectors of length period specifying the order for each season individually. In the latter case the solution of the system may not be a proper model or, if it is, its autocovariances may not be the ones used here! See the references for details.

The class of acf is not required to be one of those explicitly listed above, but it should understand their indexing conventions, similarly for sigma2.

For pure autoregression, q=0, the arguments h and sigma2 are ignored. TODO: add sigma2 (if supplied) to the returned list?

Compute h from parameters

pcarma_h_lazy: h(t,i) are the coefficients in infinite the moving average representation of the pc.arma model. The calculations use formula (4.4) from my paper (or elsewhere) with internal storage (in an slMatrix) of calculated results (for i<maxlag) and recursive calls to itself. So, it is not necessary to compute h(t,i) in any particular order.

Infinite MA coefficients(h)

pcarma_h Function to create a function for lazy computation of h(t,i) in pc.arma models

Takes a matrix of h(t,i) coefficeints and returns a function that calculates h(t,i) from my paper xxx. The returned value can be used in the same way as that of pcarma_h_lazy.

Value

for pcarma_acvf_lazy

a function taking two arguments t and k such that for scalar t and k the call f(t,k) will return EX(t)X(t-k). If either of the arguments is a vector, then f(t,k) returns a matrix of size (length(t),length(k)) containing the respective autocovariances.

for pcarma_h_lazy

a function, say h. In calls to h, if both arguments are scalars h(t,i) returns h_{t,i}. If at least one of the arguments is a vector a matrix of values of h is returned.

for pcarma_acvf_system

a list with two components representing the linear system:

A: The (p+1)\mbox{period}\times(p+1)\mbox{period} matrix of the system, an object of class "matrix".
b: The right-hand side of the system, a vector of length (p+1)\mbox{period}, an object of class "vector".

A^{-1}b can be used to get a vector of the autocovariances in the following order (d is the period, p is the maximal AR order):

K(1,0),...,K(d,0), K(1,1),...,K(d,1),...,K(1,p),...,K(d,p).

for pcarma_param_system

A list with components representing the linear system and the AR and MA orders:

A: The matrix of the system
b: The right-hand side of the system
p: The AR order
q: The MA order

A^{-1}b will return a vector of the parameters of the pc-arma model: all parameters for the first season, followed by all parameters for the second seasons and so on. For each season the parameters are in the following order (s is the current season, d is the period, p[s] and q[s] are the corresponding AR and MA orders):

\sigma^2(s), \phi(s,1),...,\phi(s,p[s]),\theta(s,1),...,\theta(s,q[s]).

for pcarma_h

a function, say h. In calls to h, if both arguments are scalars h(t,i) returns h_{t,i}. If at least one of the arguments is a vector a matrix of values of h is returned. Analogous to pcarma_h_lazy.

Note

for pcarma_acvf_lazy: The recursion may become extremely slow for lags greater than maxlag. If large lags are likely to be needed the argument maxlag should be used to increase the internal storage. The default for maxlag currently is 100.

Author(s)

Georgi N. Boshnakov

References

Examples

## periodic acf of Lambert-Lacroix
data(ex1f)
(pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt"))
## find the parameters
s3 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2)
coef3 <- solve(s3$A, s3$b)
pcarma_unvec(list(p = 2, q = 0, period = 2, param = coef3))

## actually, the model is PAR(1,2):
s3a <- pcarma_param_system(pc3, NULL, NULL, c(1, 2), 0, 2)
coef3a <- solve(s3a$A, s3a$b)
pcarma_unvec(list(p = c(1,2), q = 0, period = 2, param = coef3a))


## prepare test parameters for a PAR(2) model with period=2.
##   (rounded to 6 digits from the above example.
m1 <- rbind(c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )
m2 <- rbind(c(1, 0, 0), c(1, 0, 0) )
testphi <- slMatrix(init = m1)
testtheta <- slMatrix(init = m2)
si2 <- PeriodicVector(c(0.3439000, 0.1049724)) #     # or si2 <- c(1,1)

## acf from parameters
myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 110)
myf(1,4)        # compute a value
a1 <- myf(1:2,0:9)    # get a matrix of values

## h from parameters
h <- pcarma_h_lazy(testphi, testtheta, 2, 2, 2)
h(3, 2)           # a scalar
h1 <- h(1:2, 1:4) # a matrix

## compute acvf from parameters
( acfsys <- pcarma_acvf_system(testphi, testtheta, si2, 2, 0, 2) )
acfvec <- solve(acfsys$A, acfsys$b)
acf1 <- slMatrix(acfvec, period = 2)

## TODO: examples wirh q != 0

Functions for work with a simple list specification of pcarma models

Description

Handle a simple list specification of pcarma models. Functions to convert to and from a representation appropriate for handing on to optimisation functions.

Usage

pcarma_prepare(model, type)
pcarma_unvec(model)
pcarma_tovec(model)

Arguments

model

specification of a pcarma model, a list, see Details.

type

not used.

Details

These functions work with a specification of a pcarma model as a list with components period, p, q, param, phi, theta and si2, see also section ‘Values’. The functions do not necessarily need or examine all these components.

Argument model is a list with components as accepted by pcarma_prepare. Details are below but the guiding rule is that there are sensible defaults for absent components.

pcarma_prepare gives a standard representation of model, in the sense that it ensures that the model has components period, p and q, such that p and q are vectors of length period. pcarma_prepare does not examine any other components of the model. (TODO: do the same for the innovation variance?)

If model$period is NULL, pcarma_prepare sets it to the length of the longer of model$p and model$q. If model$p is a scalar it is extended with rep(model$p, period). Missing or NULL model$p is equivalent to model$p = 0. model$q is processed analogously.

The net effect is that period, p and q will be set as expected as long as period is given or at least one of the other two is of length equal to the period. A warning is issued if period <= 1 (it is all too easy to give scalar values for p and q and forget to set the period, in which case period will be deduced to be one).

A number of functions (including pcarma_tovec and pcarma_unvec) dealing with the list representation of pcarma models start by calling pcarma_prepare to avoid the need for handling all possible cases.

pcarma_tovec returns a list with components p, q and param, where param is a numeric vector containing the pcarma parameters and the innovations variances and thus is suitable for optimisation functions. Notice that it is component param that is a vector. The reason that pcarma_tovec returns a list, is that the caller may need to do further work before calling a generic optimisation function. For exampe, it may wish to dop the variances from the vector.

pcarma_unvec(model) performs the inverse operation. It takes a list like that produced by pcarma_tovec and converts it to a detailed list containing the components of the model.

Value

for pcarma_unvec, a list with components:

p

autoregressive orders, numeric vector

q

moving average orders, numeric vector

si2

innovation variances

phi

autoregressive parameters

theta

moving average parameters

for pcarma_tovec, a list with components:

p

autoregressive order

q

moving average order

param

parameters of the model, a numeric vector. TODO: give the order of the parameters in the vector!

for pcarma_prepare, a list as pcarma_unvec, see also Details.

Note

The specification and the functions were created ad hoc to get the computations going and are not always consistent with other parts of the package.

Author(s)

Georgi N. Boshnakov

Fit PAR models using least squares

Description

Fit PAR models using least squares. The model may contain intercepts and linear trends, seasonal or non-seasonal.

Usage

pclsdf(x, d, lags = integer(0), sintercept = TRUE, sslope = FALSE,
       intercept = FALSE, slope = FALSE, xreg, contrasts = NULL,
       seasonof1st = NULL, coefonly = FALSE)

Arguments

x

time series, a numeric vector.

d

period, an integer.

lags

an integer vector, typically 1:p, where p is the order of the autoregression. The same lags are used for all seasons.

sintercept

if TRUE include seasonal intercepts.

sslope

if TRUE include seasonal linear trend.

intercept

if TRUE include non-seasonal intercept.

slope

if TRUE include non-seasonal linear trend.

xreg

additional regressors, not used currently.

contrasts

contrasts to use for the seasons factor variable.

seasonof1st

season of the first observation in the time series, see Details.

coefonly

if TRUE, return only the parameters of the fitted model, otherwise include also the object returned by lm.

Details

This function fits PAR models by the method of least squares. Seasonal intercepts are included by default. Non-seasonal intercepts are available, as well as seasonal and non-seasonal linear trend. Separate arguments are provided, so that any combination of seasonal and non-seasonal intercepts and slopes can be specified.

If coefonly is TRUE, pclsdf returns only the estimated parameters, otherwise it includes additional statistical information, see section Note for the current details.

Value

A list with the components listed below. Some components are present only if included in the model specification.

par

the PAR coefficients, a matrix with a row for each season.

sintercept

(if specified) seasonal intercepts, a numeric vector.

sigma2hat

innovation variances.

formula.char

the formula used in the call of lm, a character string.

fit

(if coefonly = FALSE) the fitted object obtained from lm.

Note

Currently, pclsdf prepares a model formula according to the specification and calls lm to do the fitting. Component "fit" in the result (available when coefonly = FALSE) contains the raw fitted object returned by lm. Statistical inference based on this object would, in general, not be justified for correlated data.

todo: currently some of the parameters are returned only via the fitted object from lm.

Author(s)

Georgi N. Boshnakov

Examples

## data(dataFranses1996)
cu <- pcts(dataFranses1996[ , "CanadaUnemployment"])
cu <- window(cu, start = availStart(cu), end = availEnd(cu))

pclsdf(cu, 4, 1:2, sintercept = TRUE)

pclsdf(austres, 4, lags = 1:3)
pclsdf(austres, 4, lags = 1:3, sintercept = TRUE)
pclsdf(austres, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE)

x <- rep(1:4,10)
pclsdf(x, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE)

## this is for the version when contrasts arg. was passed on directly to lm.
## tmp1 <- pclsdf(austres, 4, lags = 1, sintercept = FALSE, sslope = TRUE,
##                contrasts = list(Season = "contr.sum" ))

Fit a periodically integrated autoregressive model

Description

Fit a periodically integrated autoregressive model.

Usage

pclspiar(x, d, p, icoef = NULL, parcoef = NULL, sintercept = FALSE,
         seasonof1st = 1, weights = TRUE, itol = 1e-07, maxniter = 1000)

Arguments

x

time series.

d

period.

p

order of the model, a positive integer, see Details.

icoef

initial values for the periodic integration coefficients. If missing or NULL suitable values are computed.

parcoef

not used currently.

sintercept

if TRUE include seasonal intercepts.

seasonof1st

season of the first observation.

weights

if TRUE, use periodic weights in the nonlinear least squares, see Details.

itol

threshold value for the stopping criterion.

maxniter

maximum number of iterations.

Details

This function fits a periodically integrated autoregressive model using non-linear least squares. The order of integration is one and the order of the periodically correlated part is p - 1. So, p must be greater than or equal to one.

If weights = TRUE the non-linear optimisation is done with weights inversely proportional to the innovation variances for the seasons, otherwise the unweighted sum of squared residuals is minimised.

Value

a list currently containing the following elements:

icoef

coefficients of the periodic integration filter.

parcoef

coefficients of the PAR filter.

sintercept

seasonal intercepts.

sigma2hat

innovation variances.

Author(s)

Georgi N. Boshnakov

References

Franses PH (1996). Periodicity and Stochastic Trends In Economic Time Series. Oxford University Press Inc., New York.

Franses PH, Paap R (2004). Periodic Time Series Models. Oxford University Press Inc., New York.

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Examples

## see also the examples for fitPM()
ts1 <- window(dataFranses1996[ , "CanadaUnemployment"],
              start = c(1960, 1), end = c(1987, 4))
pclspiar(ts1, 4, p = 1, sintercept = TRUE)
pclspiar(ts1, 4, p = 2, sintercept = TRUE)

Create objects from periodic time series classes

Description

Create objects from periodic time series classes.

Usage

pcts(x, nseasons, start, ..., keep = FALSE)

Arguments

x

a time series.

nseasons

number of seasons. This argument is ignored by some methods.

start

the starting time of the time series, can be a (cycle, season) pair or any object that can be converted to datetime.

keep

if TRUE and x is from class "ts", "mts", "zoo", or "zooreg", create a periodic object inheriting from that class.

...

further arguments to be passed on to methods.

Details

pcts creates periodic time series objects inheriting from "PeriodicTimeSeries". The particular class depends on arguments x and, in some cases, keep. The idea is that in normal use the user does not care about the particular class. See section ‘Methods’ for further details.

Familiar functions from base-R work with the objects created by pcts. The help page window describes such methods and gives examples.

There are also methods for as for conversion to and from the time series classes defined in package pcts.

Value

an object inheriting from "PeriodicTimeSeries", the defaults are "PeriodicTS" for univariate and "PeriodicMTS" and for multivariate time series.

Methods

signature(x = "numeric", nseasons = "missing")
signature(x = "numeric", nseasons = "numeric")
signature(x = "numeric", nseasons = "BasicCycle"): Creates an object of class "PeriodicTS", the native class for univariate periodic time series in package "pcts".
signature(x = "matrix", nseasons = "missing")
signature(x = "matrix", nseasons = "numeric")
signature(x = "matrix", nseasons = "BasicCycle"): Creates an object of class "PeriodicMTS", the native class for multivariate periodic time series in package "pcts".
signature(x = "data.frame", nseasons = "ANY"): Currently this just converts x to matrix and calls pcts recursively. See the methods with x = "matrix" in the signature.
signature(x = "ts", nseasons = "missing")
signature(x = "ts", nseasons = "numeric"): If keep = TRUE creates an object of class "PeriodicTS_ts", otherwise the result is from "PeriodicTS". The number of seasons is taken from the "mts" object.
signature(x = "mts", nseasons = "missing")
signature(x = "mts", nseasons = "numeric"): If keep = TRUE creates an object of class "PeriodicMTS_ts", otherwise the result is from "PeriodicMTS". The number of seasons is taken from the "ts" object.
signature(x = "xtsORzoo", nseasons = "missing"): x needs to be a regular time series, possibly with missing values for some times (technically, zoo::is.regular(x) should give TRUE). For daily time series, the cycle is taken to be day of week or a subcycle of it, most commonly Monday-Friday. The implementation of this method is incomplete but for daily data should work as described.

Author(s)

Georgi N. Boshnakov

Examples

## convert a ts object, no need for further info
pcts(AirPassengers, 12)

## numeric
v24 <- rnorm(24)
pcts(v24, nseasons = 4)          # generic seasons
pcts(v24, nseasons = BuiltinCycle(4)) # Quarter/Year
ts1 <- pcts(v24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates

## select subset of the seasons
window(ts1, seasons = 3:4)

## matrix, multivariate pcts
m24 <- matrix(v24, ncol =3)
colnames(m24) <- c("A", "B", "C")
pcts(m24, nseasons = 4)          # generic seasons
pcts(m24, nseasons = BuiltinCycle(4)) # Quarter/Year
mts1 <- pcts(m24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates
mts1

## select subset of the seasons for mutivariate
window(mts1, seasons = 3:4)

Deprecated Functions and classes in Package pcts

Description

These functions and classes are marked for removal and are provided temporarily for compatibility with older versions of package pcts only. Use the recommended renamed or new functions instead.

Class "FiveDayWeekCycle" is deprecated, use BuiltinCycle(5) to create objects with equivalent functionality, see BuiltinCycle.

Details

mCpar: has been renamed to sim_parCoef
sim_arAcf: has been renamed to sim_parAcvf

Periodic time series objects for examples

Description

Periodic time series objects for examples and tests. These objects are from classes defined in package “pcts” and as a consequence are not suitable for access with data().

Usage

pcts_exdata(x, envir = parent.frame())

Arguments

x

a character vector giving the names of objects. If missing, all available objects will be created. Can also be NA. In that case no objects are created and the names of all available objects are returned.

envir

environment where the objects are put, the default is the environment of the caller.

Details

The requested objects are created and put in envir. Its default is the environment of the caller, which should be sufficient in most use cases.

The following objects are currently available: ap, ap7to9, pcfr, pcfr2to4.

Value

if x is NA, the names of the available objects. Otherwise the function is called for the side effect of creating objects in envir and the return value (the names of the created objects) is usually discarded.

Examples

## the objects are created with something like:
ap <- pcts(AirPassengers)
ap7to9 <- window(ap, seasons = 7:9)

pcfr <- pcts(dataFranses1996)
pcfr2to4 <- pcfr[2:4]

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

lagged: slMatrix
date: date
as.Date: as.Date

Functions for some basic operations with seasons

Description

Functions for some basic operations with seasons.

Usage

pdSafeParOrder(p)

Arguments

p

autoregression order, a vector of integers.

Details

pdSafeParOrder(p) modifies the periodic AR order specified by vector p. The modified order is such that the correspondence between autocovariances and partial autocorrelations is one-to-one, see the references for details.

Value

a vector of integers

Author(s)

Georgi N. Boshnakov

References

Lambert-Lacroix S (2000). “On periodic autoregressive process estimation .” IEEE Transactions on Signal Processing, 48( 6 ), pp. 1800-1803.

Lambert-Lacroix S (2005). “ Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(6), pp. 423-435.

Examples

pdSafeParOrder(c(0,2))
pdSafeParOrder(c(2,3))

McLeod's test for periodic autocorrelation

Description

Performs McLeod's test for periodic autocorrelation.

Usage

periodic_acf1_test(acf, nepochs)

Arguments

acf

sample periodic autocorrelation function

nepochs

the number of epochs used to get the acf

Details

The test statistic is a scaled sum of squares of lag 1 sample periodic autocorrelation coefficients, see McLeod (1993), eq. (5). The distribution is approximately chi-square under the null hypothesis of no periodic autocorrelation.

Value

A list containing the following components:

statistic

the value of the test statistic.

pvalue

the p-value associated with the test statistic.

Author(s)

Georgi N. Boshnakov

References

McLeod AI (1993). “Parsimony, model adequacy and periodic correlation in time series forecasting.” Internat. Statist. Rev., 61(3), 387-393.

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.

McLeod AI (1995). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 16(6), 647-648. doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).

Convert between periodic centering and intercepts

Description

Convert a periodic mean to periodic intercept and vice versa.

Usage

permean2intercept(mean, coef, order, nseasons = nrow(coef))

intercept2permean(intercept, coef, order, nseasons = nrow(coef))

Arguments

mean

periodic mean, numeric.

coef

PAR coefficients, matrix.

order

PAR order, vector of positive integers.

nseasons

number of seasons, a.k.a. period.

intercept

periodic intercepts, numeric.

Details

A PAR model can be written in mean corrected or intercept form. permean2intercept calculates the intercepts from the means, while intercept2permean does the inverse (means from intercepts).

No check is made for periodic stationarity of the model. Converting from mean corrected to intercept form allways succeeds and in fact the means do not need to be means. In the opposite direction there may be problems due to unit roots and similar features.

Value

a numeric vector

Author(s)

Georgi N. Boshnakov

Examples

mu <- c(1, 2)
pm1 <- PeriodicArModel(matrix(c(0.5, 0.5), nrow = 2), order = rep(1, 2), sigma2 = 1, mean = mu)

cc <- permean2intercept(mu, pm1@ar@coef, c(1,1))
cc
intercept2permean(cc, pm1@ar@coef, c(1,1))

d <- 4
mu <- 1:d
co <- rep(0.5, d)
pm1 <- PeriodicArModel(matrix(co, nrow = d), order = rep(1, d), sigma2 = 1, mean = mu)

cc <- permean2intercept(mu, pm1@ar@coef, order = rep(1, d))
cc
intercept2permean(cc, pm1@ar@coef, order = rep(1, d) )

Compute the multi-companion form of a per model

Description

Compute the multi-companion form of a per model.

Usage

permodelmf(permodel, update = TRUE)

Arguments

permodel

a model.

update

If TRUE store the multi-companion form in permodel and return the whole model, otherwise simply return the multi-companion form.

Details

todo:

Value

the multi-companion form of the model or the updated model, as described in Details.

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Convert PIAR coefficients to PAR coefficients

Description

Convert PIAR coefficients to PAR coefficients

Usage

pi1ar2par(picoef, parcoef)
piar2par(picoef, parcoef)

Arguments

picoef

coefficients of the periodic integration filter, a numeric vector or matrix, see Details.

parcoef

coefficients of the periodically correlated part of the model.

Details

These functions expand periodic filters represented in multiplicative form. The non-periodic analogue of the operation of these functions is representing a multiplicative filter like (1-B)(1-aB), where B is the backward shift operator, by the single filter 1 - (1+a)B + aB^2, which is just a product of the polynomials, 1-B and 1 - aB.

In the non-periodic case however this operation is not, in general, equivalent to multiplication of the corresponding polynomials. It is also not commutative.

pi1ar2par converts PIAR(1) model coefficients specified as a set of coefficients corresponding to a periodic unit root and PAR coefficients to coefficients for a single filter.

piar2par does the same but admits higher order periodic integration.

picoef is a matrix, specifying one or more first order periodic unit root filters. Each column contains the coefficients of one filter. If there is only one filter, its coefficients can be given as a numeric vector.

The filters are applied from right to left, in the sense that first the PAR filter is applied to the time series, then the filter specified by the last column and so on.

Value

a matrix, whose i-th row contains the coefficients for the i-th season.

Author(s)

Georgi N. Boshnakov

Examples

## Lina's example
parcoef    <- rbind(c(0.5, -0.06), c(0.6, -0.08),
                    c(0.7, -0.1),  c(0.2, 0.15) )
picoef1    <- c(0.8, 1.25, 2, 0.5)
parcoef2   <- pi1ar2par(picoef1, parcoef)

picoef2    <- c(4, 0.25, 5, 0.2)
coefper2I2 <- pi1ar2par(picoef2, parcoef2)

McLeod-Ljung-Box test for periodic white noise

Description

Compute the McLeod-Ljung-Box test statistic for examining the null hypothesis of periodic white noise.

Usage

pwn_McLeodLjungBox_test(acf, nepoch, use = 1:maxlag,
                 maxlag = ncol(as.matrix(acf)) - 1,
                 period = nrow(as.matrix(acf)), fitdf = numeric(period))

Arguments

acf

the sample periodic autocorrelation function of the time series.

nepoch

number of cycles used in computing the acf.

use

number of lags to use, may be a vector.

maxlag

maximal lag.

period

number of seasons in a cycle.

fitdf

degrees of freedom corrections for the number of estimated parameters, see Details.

Details

The McLeod-Ljung-Box test can be used to test the null hypothesis of periodic white noise.

If acf contains sample autocorrelations of residuals from a fitted model, a correction of the degrees of freedom is strongly recommended.

Argument fitdf is a vector specifying how may degrees of freedom to subtract for each season. In the case of PAR models fitdf can be set to the PAR orders.

The value of the statistic is set to NA where the correction for degrees of freedom results in negative numbers.

Value

A list containing the following components:

statistic

the value of the test statistic for each lag specified by use.

df

the corresponding degrees of freedom

Note

TODO: Consolidate this and similar tests!

There is a typo in McLeod (1994), eq. (4.5), noted by (McLeod 1995).

Author(s)

Georgi N. Boshnakov

References

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.

McLeod AI (1995). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 16(6), 647-648. doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).

Methods for seqSeasons() in package pcts

Description

Methods for seqSeasons() in package pcts.

Methods

signature(x = "BasicCycle")
signature(x = "Cyclic")
signature(x = "VirtualPeriodicModel")

Methods for `sigmaSq` in package pcts

Description

Methods for sigmaSq in package pcts.

Methods

signature(object = "PeriodicIntegratedArmaSpec")
signature(object = "PeriodicInterceptSpec")

Create a random periodic autocovariance function

Description

Select randomly a periodic autoregression model and return the periodic autocovariances associated with it.

Usage

sim_parAcvf(period, order, sigma2)

Arguments

period

the period, a positive integer.

order

the AR order, a vector of non-negative integers.

sigma2

the variances of the innovations, a numeric vector of length period (todo: or one?).

Details

Uses sim_parCoef() to generate a random PAR model.

Value

an object of class "matrix". In addition, the specification of the model is in attribute "model" which is a list with the following components:

ar

a matrix, the coefficients of the PAR model,

sigma2

numeric, the innovation variances,

order

the PAR order.

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Examples

sim_parAcvf(2, 5)
sim_parAcvf(3, 5)

res <- sim_parAcvf(2, 6)
res
slMatrix(res)[3, 4, type = "tt"]

res <- sim_parAcvf(2, 4)
attr(res, "model")
acv <- res[ , ] # drop attributes

acv[2, 1 + 0]
acv[2, 1 + 1]
slMatrix(acv)[2, 0]
slMatrix(acv)[2, 1]
slMatrix(acv)[3, 4, type = "tt"]
slMatrix(acv)[1:2, 1:2, type = "tt"]
slMatrix(acv)[1:4, 1:4, type = "tt"]

## TODO: need method for autocorrelation()
## pc.acrf(acv)

## TODO: these need changing, after the change of the return values of sim_parAcvf
## pc.fcoeffs(acv, 2)
## pc.fcoeffs(acv, 3)
## pc.fcoeffs(acv, 4)
pcts:::calc_predictionCoefficients(acv, c(2, 2))
pcts:::calc_predictionCoefficients(acv, c(3, 3))
pcts:::calc_predictionCoefficients(acv, c(4, 4))

Generate a periodic autoregression model

Description

Generate a periodic autoregression model, possibly integrated.

Usage

sim_parCoef(period, n.root, sigma2 = rep(1, period), ...)

Arguments

period

number of seasons in a cycle.

n.root

number of non-zero roots, see details.

sigma2

variances of the innovations.

...

additional arguments to be passed down to sim_pcfilter

Details

sim_parCoef uses the multi-companion method to generate the model. The function is essentially a wrapper for sim_pcfilter.

The order of the filter is set to n.root for each season. Part of the spectral information may be specified with the "..." arguments, see sim_pcfilter and sim_mc for a discussion of this.

Value

a periodic autoregression model as a list with elements:

ar

a matrix whose ith row contains the coefficients for the iseason,

sigma2

the innovation variances, a numeric vector.

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Examples

sim_parCoef(2, 4)                    # 2 seasons
sim_parCoef(2, 4, sigma2 = c(2, 4))
sim_parCoef(2, 1)
sim_parCoef(4, 2)                    # 4 seasons

sim_parCoef(period = 4, n.root = 6,
    eigabs = c(1, 1, 1, 0.036568887, 0.001968887),
    type.eigval = c("cp", "r", "r", "r",  "r"),
    eigsign     = c(pi/2,   1,  -1,   1,   -1))

Simulate periodically correlated ARMA series

Description

Simulate a realization of a periodically correlated arma model or a continuation of an existing series. Initial values may be given too.

Usage

sim_pc(model, n = NA, randgen = rnorm, seasonof1st = 1, nepochs = NA,
              n.start = NA, x, eps, nmean = NULL, nintercept = NULL, ...)

Arguments

model

a list with elements phi, theta, p, q, period, mean, intercept, specifying the model.

n

length of the series.

randgen

random number generator as required by sim_pwn.

seasonof1st

season of the first value.

nepochs

number of epochs; if nepochs is given, then n is computed as nepochs * period.

n.start

burn-in number; generate \code{n.start + n} observations and discard the first n.start of them, see Details.

x

initial or before values, see Details.

eps

innovations, see Details.

nmean

a vector of length n of means, see Details.

nintercept

a vector of length n of intercepts, see Details.

...

any additional arguments to be passed on to sim_pwn.

Details

Argument x can be used to specify two types of initialisation values - ‘before’ and ‘init’. They are used similarly in computations but ‘before’ values are not included in the result, while ‘init’ values are (unless dropped due to n.start). ‘Before’ values provide a convenient way to simulate continuation trajectories for a time series, for example for simulation based prediction intervals.

If x is "numeric", it represents ‘before’ values. Alternatively, x can be a list with components "before" and "init".

Innovations are usually generated with the random number generator specified by randgen (with default rnorm) and the ... parameters by a call to the function sim_pwn, see the documentation for sim_pwn for various ways to control the distribution of the generated sequence.

The innovations can also be generated in advance and supplied using argument eps. If eps is numeric, it is taken to represent the innovations. Alternatively, eps can be a list with the innovations in component "main". This list may also contain components "before" and/or "init" specifying ‘before’ or ‘initial’ values, with interpretation as for x.

nintercept can be used to specify trend representing the effect of time and/or covariates. As for eps, if it is numeric it is taken to represent the main values. It can also be a list with components before, init, and main.

To avoid ambiguity, let's reiterate that before values are past values of the corresponding quantity (before the start of the simulated series), while init values are "initial" values. In particular, if initial values are specified for x, these will form the start of the generated series (unless n.start leads to them being discarded).

If before values are specified for the series and the innovations, then they play a role analogous to that of initial values, so it does not make much sense to supply also initial values.

The function effectively does the following. innov is generated if not supplied, a vector of innovations is created eps <- c(innovbefore,innovinit,innov), a vector x is created of the same length as eps, and initialised with xbefore and xinit. If there are no initial or before values, these are assumed to be 0. The remaining values of x are filled using the pc-arma equations. Finally, the xbefore values are discarded as well as the first n.start values.

n.start should usually be a multiple of the period since otherwise the first observation in the returned vector will not correspond to seasonof1st.

sim_pc deals mainly with the interpretation of the parameters. The actual computations are done by pc.filter. Moreover, sim_pc does not look at the model. It knows only about model$period and uses it to compute n if n is not specified. (It probably should not care even about this.)

Value

numeric, the simulated time series

To do

option to return the innovation sequence; option to include the before values.

option to return the season of the first value in the returned series (it may be different from seasonof1st due to n.start).

Author(s)

Georgi N. Boshnakov

Examples

m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )
testphi <- slMatrix( init = m1 )

m2 <- rbind( c(1, 0, 0), c(1, 0, 0) )
testtheta <- slMatrix( init = m2 )

## phi and theta are slMatrix here.
mo1 <- list(phi = testphi, theta = testtheta, p = 2, q = 2, period = 2)
set.seed(1234)
a1 <- sim_pc(mo1, 100)

## phi and theta are ordinary matrices here.
mo2 <- list(phi = m1[ , 2:ncol(m1)], theta = m2[ , 2:ncol(m2)], p = 2, q = 2, period = 2)
set.seed(1234)
a2 <- sim_pc(mo2, 100)
identical(a1, a2)

## Lina's PAR model
parcoef    <- rbind(c(0.5, -0.06), c(0.6, -0.08),
                    c(0.7, -0.1),  c(0.2, 0.15) )
picoef1    <- c(0.8, 1.25, 2, 0.5)
parcoef2   <- pi1ar2par(picoef1, parcoef)

picoef2    <- c(4, 0.25, 5, 0.2)
coefper2I2 <- pi1ar2par(picoef2, parcoef2)

#### specify the model using multi-companion approach
mc2I2       <- mcompanion::mc_from_filter(coefper2I2)
co2I2       <- eigen(mc2I2)$vectors
co2I2
m2I2 <-  mcompanion::sim_pcfilter(period = 4, n.root = 4,
                 eigabs = c(1, 0.036568887, 0.001968887),
                 eigsign = c(1, 1, -1),
                 len.block = c(2, 1, 1),
                 type.eigval  =  c("r", "r", "r"),
                 co = cbind(co2I2[ ,1], rep(NA, 4), co2I2[,3:4]))
m2I2$pcfilter
perunit2mc  <- sim_pc(list(phi = m2I2$pcfilter, p = 4, q = 0, period = 4), 500)
plot(perunit2mc)
plot(perunit2mc, type = "p")

# todo: give example with sigmat^2 !!!

Simulate periodic white noise

Description

Simulate periodic white noise.

Usage

sim_pwn(n = 100, period = NA, seasonof1st = 1, scale = NULL, 
        shift = NULL, f = rnorm, ...)

Arguments

n

length of the generated sample.

period

number of seasons in an epoch.

seasonof1st

season of the first observation in the result.

scale

scale the series by this amount, a vector of length period or 1.

shift

shift the series by this amount, a vector of length period or 1.

f

a function or list of functions to generate random numbers.

...

arguments for the random number generator(s) specified by f.

Details

First a series, say x, of random numbers is generated as requested by the argument f. Then, if shift and/or scale are supplied, the values are modified as follows:

y_t = shift_{k} + scale_{k} x_t

where k is the season corresponding to time t. The vector y is returned.

If f is a single a function (or name of a function), then the series is generated (effectively) by the call f(n,...).

The argument f may also be a list whose kth element is itself a list specifying the random number generator for the kth season. The first element being the function (such as rnorm) and the remaining elements being parameters for that function. Parameters common to all seasons may be supplied through the ... argument.

The argument period may be omitted. In that case it is inferred from f and/or the lengths of shift and scale. Currently there is no check for consistency here.

The arguments shift and scale may be used to specify simple linear transformations of the generated values, possibly different for the different seasons. Each of them should be a vector of length period or one.

seasonof1st can be used to request the simulated time series to start from a season other than the first one. Note that whatever the value of seasonof1st, the first elements of scale, shift and f (if a list) are taken to refer to season one.

Value

A vector of length n representing a realization of a periodic white noise series. The season of the first observation is seasonof1st.

Level

0 (base)

Author(s)

Georgi N. Boshnakov

Examples

## three equivalent ways to specify periodic white noise with
## normal innovatios, 2 seasons, s.d. = 0.5 for season 1, and 2 for season 2
sim_pwn(100, f = rnorm, scale = c(0.5, 2))
sim_pwn(n = 100, scale = c(0.5, 2))  # rnorm is the default generator
sim_pwn(100, f = list(c(rnorm, 0, 0.5), c(rnorm, 0, 2)))

Functions for some basic operations with seasons

Description

Functions for some basic operations with seasons.

Usage

toSeason(t, period, t1 = 1, from = 1)
toSeasonPair(t, s, period, ...)
ttTosl(r, period)
ttmatToslPairs(i, j, period)

Arguments

r

covariance matrix, see ‘Details’.

t

a vector of integers, representing times.

s

a vector of integers, representing times.

period

the number of seasons.

t1

time corresponding to the first season, an integer number.

from

1 or 0, depending on whether the season numbers start from 1 or 0.

i

a vector of integers.

j

a vector of integers.

...

todo: describe!

Details

ttmatToslPairs(i,j,period) transforms time-time pairs to season-lag pairs. The time pairs are obtained by pairing each element of i with each element of j. A four column matrix is created with one row for each pair (t,s), such that t=i[m] and s=j[n] for some m and n. The row is m, n, s, l, where (s,l) is the season-lag pair corresponding to (t,s).

ttTosl(r,period) converts autocovariances given in a covariance matrix (i.e. in “tt” form) to the “sl” form. The result is a period x (maxlag+1) matrix, where maxlag is the maximal lag available in r. Entries for which no values are available are filled with NA's. Warning is given if contradictory entries are found (i.e. if r is not from a periodically correlated process with the given period).

toSeason(t,period,t1=1,from=1) returns the season corresponding to t. t1 is a time (integer) whose season is the first season, from is 1 if the numbering of seasons is 1,2,...,period, or 0 if the numbering of seasons is 0,1,...,period-1. Other values for from are not admissible (but not checked). Note: some of the functions in this package implicitly assume that t1=1 and from=1.

toSeasonPair(t,s,period) converts the “tt” pair t,s to “sl” pair and returns the result in the form of a list with elements season and lag. Currently t and s must be scalars.

pc.omitneg helps to implement dropping of negative indices in season-lag objects. It returns its first argument, lags, if all of its elements are non-negative. Otherwise, all elements of lags must be non-positive. In this case the function creates the vector 0:maxlag and drops the elements specified by lags. Note that the default indexing will not work properly since zero elements in an index are omitted (and there are such indices in season-lag objects).

Value

for ttmatToslPairs, a matrix with four columns;

for ttTosl, a matrix with period rows;

for toSeason(t,period,t1=1,from=1), a vector of integers;

for toSeasonPair(t,s,period), a list with elements season and lag;

for pc.omitneg, a vector of lags (non-negative integers).

Note

2013-10-24 - Corrected the description of the return value of ttmatToslPairs. It incorrectly stated that the first two columns are "tt" pair (they are actually indices in i and j).

Author(s)

Georgi N. Boshnakov

References

Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.

Examples

# ttmatToslPairs
ttmatToslPairs(3, 3, 4)  # 1, 1, 3, 0
ttmatToslPairs(3, 2, 4)  # 1, 1, 3, 1

ttmatToslPairs(1:4, 1:4, 4)

ttmatToslPairs(3:4, 3:4, 4)

# ttTosl -  :todo:

# toSeason
toSeason(1:10, 4)           # 1 2 3 4  1 2 3 4  1 2
toSeason(1:10, 4, from = 0) # 0 1 2 3  0 1 2 3  0 1

## first data is for 3rd quarter
toSeason(1:10, 4, t1 = 3)  # 3 4 1 2 3 4 1 2 3 4

# toSeasonPair
toSeasonPair(3, 3, period=4) # season=3, lag = 0
toSeasonPair(8, 8, period=4) # season=4, lag = 0

toSeasonPair(3, 2, period=4) # season=3, lag = 1
toSeasonPair(7, 6, period=4) # same

#### # pc.omitneg
#### pc.omitneg(0:5,10) # 0:5, unchaged since all values >= 0
#### 
#### pc.omitneg(-(0:5),10) # 6:10, works like
#### (0:10)[-(0:5 +1)]     # same
#### 
#### # don't mix positive and negative numbers in pc.omitneg
#### \dontrun{pc.omitneg(c(0,2,3,-4,5), 10)}

Methods for function tail() in package pcts

Description

Methods for function tail() in package pcts.

Methods

signature(x = "PeriodicTimeSeries")

Test for periodic integration

Description

Test if a time series is periodically integrated.

Usage

test_piar(x, d, p, sintercept = FALSE, sslope = FALSE, homoschedastic = FALSE)

Arguments

x

time series.

d

period.

p

autoregressive order, a positive integer.

sintercept

if TRUE, include seasonal intercept.

sslope

if TRUE, include seasonal slope.

homoschedastic

if TRUE, assume the innovations variance is the same for all seasons.

Details

Computes test statistics for Franses (1996) test for periodic integration of order 1. The test is based on periodic autoregression of order p, where p can be any positive integer.

Value

a list with the following components:

p

autoregressive order.

spec

values of sintercept, sslope, and homoschedastic, a named logical vector.

statistics

a matrix containing the test statistics (first row) and the corresponding p-values (second row). "LR" is not normalised, so its p-value is NA.

Note

Currently only the case p = 1 is handled, for p > 1 the statistics are set to NA. :TODO: handle this.

All statistics are computed but some p-values are not computed yet.

Author(s)

Georgi N. Boshnakov

References

Boswijk HP and Franses PH (1996). “Unit roots in periodic autoregressions.” Journal of Time Series Analysis, 17(3), pp. 221–245.

Examples

ts1 <- window(dataFranses1996[ , "CanadaUnemployment"],
              start = c(1960, 1), end = c(1987, 4))
test_piar(ts1, 4, 1, sintercept = TRUE)
pcTest(ts1, "piar", 4, 1, sintercept = TRUE) # same

test_piar(ts1, 4, 1, sintercept = TRUE, sslope = TRUE)
test_piar(ts1, 4, 1)              
test_piar(ts1, 4, 1, homoschedastic = TRUE)

Methods for `unitCycle<-` and `unitSeason<-` in package pcts

Description

Methods for `unitCycle<-` and `unitSeason<-` in package pcts.

Methods

`unitCycle<-` and `unitSeason<-` have methods with identical signatures:

signature(x = "Cyclic")
signature(x = "SimpleCycle")

Examples

qrt <- BuiltinCycle(4)
unitSeason(qrt)                 # "Quarter"
unitCycle(qrt)                  # "Year"

moreve <- new("SimpleCycle", 2)
unitSeason(moreve)             # "Season"
unitCycle(moreve)              # "Cycle"
allSeasons(moreve)             # c("Season_1", "Season_2")

## change the names
unitCycle(moreve) <- "Day"
unitSeason(moreve) <- "TimeOfDay"
allSeasons(moreve) <- c("Morning", "Evening")

unitSeason(moreve)
unitCycle(moreve) 
allSeasons(moreve)

Methods for `unitCycle` and `unitSeason` in package pcts

Description

Methods for unitCycle and unitSeason in package pcts.

Methods

unitCycle and unitSeason have methods with identical signatures:

signature(x = "ANY")
signature(x = "VirtualPeriodicModel")
signature(x = "Cyclic")
signature(x = "SimpleCycle")
signature(x = "PartialCycle")
signature(x = "OpenCloseCycle")
signature(x = "QuarterYearCycle")
signature(x = "DayWeekCycle")
signature(x = "MonthYearCycle")
signature(x = "Every30MinutesCycle")

Examples

## presidents is a quarterly time series in base-R
tsp(presidents)

pc_presidents <- pcts(presidents)
unitCycle(pc_presidents)
unitSeason(pc_presidents)

Periodic methods for base R functions

Description

Periodic methods for base R functions.

Usage

## S3 method for class 'PeriodicTS'
window(x, start = NULL, end = NULL, seasons = NULL, ...)

## S3 method for class 'PeriodicMTS'
window(x, start = NULL, end = NULL, seasons = NULL, ...)

## S3 method for class 'PeriodicTS'
na.trim(object, sides = c("both", "left", "right"), ...)

## S3 method for class 'PeriodicMTS'
na.trim(object, sides = c("both", "left", "right"), 
        is.na = c("any", "all"), ...)

## S3 method for class 'PeriodicTimeSeries'
frequency(x, ...)

## S3 method for class 'PeriodicTimeSeries'
deltat(x, ...)

## S3 method for class 'PeriodicTimeSeries'
cycle(x, ...)

## S3 method for class 'PeriodicTimeSeries'
time(x, offset = 0, ...)

## S3 method for class 'Cyclic'
start(x, ...)

## S3 method for class 'Cyclic'
end(x, ...)

Arguments

x, object

an object from the indicated periodic class.

start

numeric(2), start time.

end

numeric(2), end time.

seasons

numeric, a subset of 1:nSeasons(x).

...

Not used by these methods.

sides

which side to trim: start ("left"), end ("right"), or both ("both").

is.na

for multivariate time series: if "all", the observation at time t will be considered missing only if all variables are NA at that time. Otherwise, if "any", any variable with value NA will cause the observation at time t to be considered missing.

offset

currently ignored (:TODO:)

Details

Periodic methods for base R and other common functions for manipulation of time series. These methods work analogoulsly to their base R cousins and only the differences, if any, are discussed below.

window takes a part of x, preserving the class of the object. Argument seasons selects a subset of the seasons.

na.trim is a function defined in package zoo and re-exported by pcts. It trims NAs from one or both ends of the time series, as requested by the arguments. The arguments of the methods defined by pcts have the same meaning as those in zoo.

Value

for window and na.trim, an object from the same class as the original, representing the requested part of the time series.

for frequency, an integer number.

for deltat, a number (1/frequency).

for cycle and time, a "PeriodicTS" object.

for start and end, time of first/last observation, encoded as a pair of numbers.

Examples

pres <- pcts(presidents)
head(pres, 8)
availStart(pres)

tail(pres, 12)
availEnd(pres)

## Q3 and Q4 only
presQ3Q4 <- window(pres, seasons = 3:4)
head(presQ3Q4)

identical(na.trim(pres),
          window(pres, start = availStart(pres), end = availEnd(pres)))
## TRUE

Class zoo made S4

Description

Class zoo made S4

Objects from the Class

A virtual Class: No objects may be created from it.

S4 Class "zoo" is derived from its namesake in package zoo for use as a super class for periodic time series classes and in S4 method signatures.

Slots

.S3Class:: Object of class "character" ~~

Extends

Class "oldClass", directly.

Methods

No methods defined with class "zoo" in the signature.

Examples

showClass("zoo")

Virtual S4 class zooreg

Description

Virtual S4 class zooreg.

Objects from the Class

A virtual Class: No objects may be created from it.

S4 Class "zooreg" is derived from its namesake in package zoo for use as a super class for periodic time series classes and in S4 method signatures.

Slots

.S3Class:: Object of class "character" ~~

Extends

Class "zoo", directly. Class "oldClass", by class "zoo", distance 2.

Methods

No methods defined with class "zooreg" in the signature.

Examples

showClass("zooreg")

Periodically Correlated and Periodically Integrated Time Series

Description

Details

Author(s)

References

See Also

Examples

Methods for function$ in package 'pcts'

Description

Methods

Class BareCycle

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

See Also

Examples

Class BasicCycle

Description

Objects from the Class

Methods

Author(s)

See Also

Examples

Class "BuiltinCycle" and its subclasses in package 'pcts'

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

See Also

Examples

Create objects from class Cyclic

Description

Usage

Arguments

Value

See Also

Examples

Class "Cyclic"

Description

Objects from the Class

Slots

Methods

See Also

Examples

Class FittedPeriodicArModel

Description

Objects from the Class

Slots

Extends

Methods

Class FittedPeriodicArmaModel

Description

Objects from the Class

Slots

Extends

Methods

Fraser River at Hope, mean monthly flow

Description

Usage

Format

Details

Source

See Also

Examples

Class LegacyPeriodicFilterModel

Description

Objects from the Class

Slots

Extends

Methods

Class ModelCycleSpec

Description

Objects from the Class

Slots

Methods

Methods for function`$` in package 'pcts'

Class `"BuiltinCycle"` and its subclasses in package 'pcts'

Class `"Cyclic"`

Class `"PeriodicArmaFilter"`