Invert taking logs and differences of a time series

Description

For a series that has been logged and/or differenced, this function reverses these transformations.

Usage

Descaler(x, y = NA, Diff = 0, Sdiff = 0, Log = FALSE, Lag = NA)

Arguments

Details

The time series used as a benchmark (y) is necessary, if regular or seasonal differences have to be inversed, because the first values of this series are used to reconstruct the original values or benchmark the new series.

Author(s)

Daniel Ollech

Examples

a = ts(rnorm(100, 100, 10), start=c(2015,1), frequency=12)
b = Scaler(a, Diff=1, Log=TRUE)
Descaler(b,a, Diff=1, Log=TRUE)

Take logs and differences of a time series

Description

Logarithmise and / or difference a time series

Usage

Scaler(x, Diff = 0, Sdiff = 0, Log = FALSE)

Arguments

Details

Function is used in dsa to let the user decide whether logs and differences should be taken.

Author(s)

Daniel Ollech

Examples

a = ts(rnorm(100, 100, 10), start=c(2015,1), frequency=12)
Scaler(a, Diff=1, Log=TRUE)

Exemplary time series

Description

Three time series that have been analysed by Ollech (2021) and their seasonally and calendar adjusted variants.

Usage

daily_data

Format

An xts data set containing 3 time series:

currency_circulation

Currency in circulation in Germany, in billion Euros, sum of small denominations: i.e. 5 Euro + 10 Euro + 20 Euro + 50 Euro. Series compiled by Deutsche Bundesbank

elec_consumption

Electricity consumption in Germany in GWh. Compiled by Bundesnetzagentur (German Federal Network Agency)

no2

Nitrogen dioxide (NO2) immissions averaged over all available measuring stations in Europe that are made available by the European Environment Agency (EEA)

#'

currency_circulation_sa

Seasonally and calendar adjusted version using dsa of currency_circulation

elec_consumption_sa

Seasonally and calendar adjusted version using dsa of elec_consumption

no2_sa

Seasonally and calendar adjusted version using dsa of no2

Author(s)

Daniel Ollech

Source

Own calculations, Deutsche Bundesbank, Bundesnetzagentur, EEA

References

Ollech, Daniel (2021). Seasonal Adjustment of Daily Time Series. Journal of Time Series Econometrics (forthcoming).

Create a simple, exemplary, seasonal, daily time series

Description

Create a seasonal daily time series and its seasonal and non-seasonal components

Usage

daily_sim(
  n = 8,
  week_effect = 1,
  month_effect = 1,
  year_effect = 1,
  model = c(3, 1, 1),
  ar = c(-0.2, 0.5, 0.1),
  ma = -0.4,
  moving = T,
  week_cycles = 2,
  month_cycles = 3,
  year_cycles = 8
)

Arguments

Details

The output is an xts time series containing the time series, the true seasonally adjusted series,

the day-of-the-week seasonal component, the day-of-the-month seasonal component and the

day-of-the-year seasonal component.

Author(s)

Daniel Ollech

Examples

time_series <- daily_sim(n=4, year_effect=3)
xtsplot(time_series[,1]) # Plot of the time series
xtsplot(time_series[,3:5]) # Plot of the seasonal factors

Delete name of xts

Description

Delete name of xts

Usage

del_names(x)

Arguments

Details

This function can be helpful if one xts is created to be equal to another xts and then changed afterwards. In these cases the new xts inherits the column name of the old xts.

Author(s)

Daniel Ollech

Examples

timeseries <- dsa::daily_sim()$original # timeseries inherits name from original
colnames(timeseries)
colnames(del_names(timeseries))
y <- del_names(timeseries)
colnames(merge(timeseries, y))

Seasonally Adjust Daily Time Series

Description

Seasonally adjust daily time series using the dsa approach

Usage

dsa(
  series,
  span.start = NULL,
  model = NULL,
  Log = FALSE,
  automodel = "reduced",
  ic = "bic",
  include.constant = FALSE,
  fourier_number = 24,
  max_fourier = 30,
  s.window1 = 53,
  s.window2 = 53,
  s.window3 = 13,
  t.window1 = NULL,
  t.window2 = NULL,
  t.window3 = NULL,
  cval = 7,
  robust1 = TRUE,
  robust2 = TRUE,
  robust3 = TRUE,
  regressor = NULL,
  forecast_regressor = NULL,
  reg_create = NULL,
  reg_dummy = NULL,
  outlier = TRUE,
  outlier_types = c("AO", "LS", "TC"),
  delta = 0.7,
  model_span = NULL,
  feb29 = "sfac",
  trend_month = 3,
  outer3 = NULL,
  inner3 = NULL,
  h = 365,
  reiterate3 = NULL,
  scaler = 1e+07,
  mean_correction = TRUE,
  progress_bar = TRUE
)

Arguments

Details

This function can be used to seasonally and calendar adjust daily time series and decomposing the series into a seasonally adjusted series, a day-of-the-week, a moving holiday, a day-of-the-month and a day-of-the-year component.

If mean_correction=TRUE (default), the seasonal and calendar factors are corrected, so that over all full years, the mean of the components is 0 in additive models. They will be close to 1 if a multiplicative decomposition (i.e. Log=TRUE) is used. Deviations from 1 may result, because the mean correction is applied to the components before inverting taking logs.

For long series, the ARIMA modelling and the outlier adjustment may take a long time. It may therefore be a good idea, to specify the ARIMA model used, e.g. model=c(3,1,0). If the series does not contain influential outliers, the outlier adjustment could be skipped by setting outlier=FALSE.

See vignette for further examples.

Value

dsa returns a daily object which contains the output of the seasonal adjustment of a daily time series.

output Contains the calendar and seasonally adjusted series, original series, implicit calendar and seasonal component, and Loess based trend as an xts object

fourier_terms The number of sine and cosine terms used to model the seasonal pattern in the RegARIMA model

reg RegARIMA results

info Basic information on transformation (Log/Level), differencing and forecast horizon

stl A list of length 3, containing the STL results of the day-of-week, day-of-the-month and day-of-the-year adjustment, respectively

outlier Result of the outlier adjustment

sa_result The original series and the intermediate adjustment results after the day-of-week adjustment (s1_adjusted), calendar adjustment (s1k1_adjusted), day-of-the-month adjustment (s1k1s2_adjusted), and the final adjusted series after the day-of-the-year adjustment (seas_adj) as an xts object

sa_result2 The original series only adjusted for single components as an xts object. Namely the original series itself (original), the original only adjusted for the day-of-the week (s1_adjusted), calendar (k1_adjusted), day-of-the-month (s2_adjusted), and day-of-the-year (s3_adjusted)

sfac_result The seasonal and calendar components as an xts object. Namely, the day-of-the-week (s1_fac), calendar (cal_fac), day-of-the-month (s2_fac), and day-of-the-year component (s3_fac)

Author(s)

Daniel Ollech

References

Ollech, Daniel (2018). Seasonal adjustment of daily time series. Bundesbank Discussion Paper 41/2018.

Ollech, Daniel (2021). Seasonal Adjustment of Daily Time Series. Journal of Time Series Econometrics (forthcoming).

Examples

x = daily_sim(n=4)$original # series with length 4 years
res <- dsa(x, cval=7, model=c(3,1,0),fourier_number = 13)

Exemplary dsa outputs

Description

The dsa results for the three time series that have been analysed by Ollech (2021). Details on the specification can be found in the vignette.

Usage

dsa_examples

Format

A list containing the following three objects

cic_dsa

Results from a call to dsa() for the currency in circulation in Germany, in billion Euros, sum of small denominations: i.e. 5 Euro + 10 Euro + 20 Euro + 50 Euro. Series compiled by Deutsche Bundesbank.

elec_dsa

Results from a call to dsa() for the electricity consumption in Germany in GWh. Compiled by Bundesnetzagentur (German Federal Network Agency)

no2_dsa

Results from a call to dsa() for the nitrogen dioxide (NO2) immissions averaged over all available measuring stations in Europe that are made available by the European Environment Agency (EEA)

Author(s)

Daniel Ollech

Source

Own calculations, Deutsche Bundesbank, Bundesnetzagentur, EEA

References

Ollech, Daniel (2021). Seasonal Adjustment of Daily Time Series. Journal of Time Series Econometrics (forthcoming).

Obtain the frequency of an xts time series

Description

Estimate the number of periods per year of an xts time series

Usage

freq_xts(series)

Arguments

Author(s)

Daniel Ollech

Examples

x <- xts::xts(rnorm(100), seq.Date(from=as.Date("2010-01-01"), by="months", length.out=100))
frequency(x)

Get Original Time Series

Description

Get the original time series from a seasonal adjustment object created by the dsa function. Can deviate from the input data as missings are filled up, usually using zoo::na.locf().

Usage

get_original(daily.object, forecast = FALSE)

Arguments

Author(s)

Daniel Ollech

See Also

get_sa, get_trend

Examples

set.seed(123)
x = daily_sim(n=4)$original # series with length 4 years
res <- dsa(x, cval=7, model=c(3,1,0),fourier_number = 13)
get_original(res)

Get Seasonally Adjusted Series

Description

Get the calendar- and seasonally adjusted series from a seasonal adjustment object created by the dsa function

Usage

get_sa(daily.object, forecast = FALSE)

Arguments

Author(s)

Daniel Ollech

See Also

get_trend, get_original

Examples

set.seed(123)
x = daily_sim(n=4)$original # series with length 4 years
res <- dsa(x, cval=7, model=c(3,1,0),fourier_number = 13)
get_sa(res)

Get Trend-Cycle

Description

Calculate the trend-cycle based on a seasonally adjusted series obtained from a seasonal adjustment object created by the dsa function

Usage

get_trend(daily.object, trend_length = 93, forecast = FALSE)

Arguments

Details

If not odd the parameter trend_length is set to the next highest odd number.

Author(s)

Daniel Ollech

See Also

get_sa, get_original

Examples

set.seed(123)
x = daily_sim(n=4)$original # series with length 4 years
res <- dsa(x, cval=7, model=c(3,1,0),fourier_number = 13)
get_trend(res)

Data set for frequently used regressors

Description

Daily time series in xts format containing many regressors for holidays potentially used in the adjustment of daily time series

Usage

holidays

Format

An xts data set containing 131 regressors for the time span 1950 to 2075:

AllSaints

AllSaints, Nov 1

Ascension

Ascension

AscensionAft1Day

Captures the first day after Ascension

AscensionBef1Day

Captures the last day before Ascension

AssumptionOfMary

Assumption of Mary, Aug 15

Aug15ZZZ

Captures if Assumption of Mary, Aug 15, is a certain weekday (Monday to Sunday)

Base

Regressor made up of 0s, can be used to create other regressors

BoxingDay

Boxing Day, Dec 26

CarnivalMonday

Carnival Monday

ChristmasDay

Christmas Day, Dec 25

ChristmasEve

Christmas Eve, Dec 24

CorpusChristi

Corpus Christi

CorpusChristiAft1Day

Captures the first day after Corpus Christi

CorpusChristiBef1Day

Captures the last day before Corpus Christi

Dec24ZZZ

Captures if Dec 24 is a certain weekday (Monday to Sunday)

Dec25ZZZ

Captures if Dec 25 is a certain weekday (Monday to Sunday)

Dec26ZZZ

Captures if Dec 26 is a certain weekday (Monday to Sunday)

Dec31ZZZ

Captures if Dec 31 is a certain weekday (Monday to Sunday)

Dst

Daylight Saving Time, Spring=-1, Autumn=1

DstAutumn

Daylight Saving Time, Autumn=1

DstSpring

Daylight Saving Time, Spring=1

EasterMonday

Easter Monday

EasterMondayAft1Day

Captures the first day after Easter Monday

EasterPeriod

Captures all days from Holy Thursday to Easter Monday

EasterSunday

Easter Sunday

Epiphany

Epiphany, Jan 6

GermanUnity

German Unity, Oct 3

GoodFriday

Good Friday

HolyThursday

Holy Thursday

HolySaturday

Holy Saturday

Jan1ZZZ

Captures if Jan 1 is a certain weekday (Monday to Sunday)

Jan6ZZZ

Captures if Jan 1 is a certain weekday (Monday to Sunday)

LabourDay

Labour Day, May 1

LabourBridge

Captures the bridge days created by May 1, i.e. if surrounding days are either a Monday or Friday

MardiGras

Mardi Gras

May1ZZZ

Captures if Labour Day, May 1, is a certain weekday (Monday to Sunday)

NewYearsDay

New Years Day, Jan 1

NewYearsEve

New Years Eve, Dec 31

Nov1ZZZ

Captures if Nov 1 is a certain weekday (Monday to Sunday)

Nov1Bridge

Captures the bridge days created by Nov 1, i.e. if surrounding days are either a Monday or Friday

Oct3ZZZ

Captures if German Unity, Oct 3, is a certain weekday (Monday to Sunday)

Oct3Bridge

Captures the bridge days created by Nov 1, i.e. if surrounding days are either a Monday or Friday

Oct31ZZZ

Captures if Reformation Day, Oct 31, is a certain weekday (Monday to Sunday)

Oct31Bridge

Captures the bridge days created by Reformation Day, i.e. if surrounding days are either a Monday or Friday

Pentecost

Pentecost Monday

PentecostAft1Day

Captures the first day after Pentecost Monday

PentecostBef1Day

Captures the last day before Pentecost Monday

PentecostMonday

Alias for Pentecost Monday

PentecostPeriod

Period spanning three days from Pentecost Sunday to Tuesday after Pentecost Monday

PostNewEveSat1w

Captures Saturdays in the period from Dec 31 to Jan 6

PostNewEveSun1w

Captures Sundays in the period from Dec 31 to Jan 6

PostXmasSat1w

Captures Saturdays in the period from Dec 27 to Jan 2

PostXmasSun1w

Captures Sundays in the period from Dec 27 to Jan 2

PostXmasSat10d

Captures Saturdays in the period from Dec 27 to Jan 5

PostXmasSun10d

Captures Sundays in the period from Dec 27 to Jan 5

PreXmasSat3d

Captures Saturdays in the three days leading up to Christmas

PreXmasSun3d

Captures Sundays in the three days leading up to Christmas

ReformationDay

Reformation Day, Oct 31

ReformationDay2017

Reformation Day, Oct 31 2017 (National holiday that year)

XmasPeriodZZZ

Captures weekdays (Monday to Sunday) in the Christmas period from Dec 21 to Jan 5

Author(s)

Daniel Ollech

Source

Own calculations

Creating holiday regressor that increases linearly up to holiday and decreases afterwards

Description

Creating holiday regressor that increases linearly up to holiday and decreases afterwards

Usage

make_cal(holidays = NULL, h = 365, original = NA, original2 = NA)

Arguments

Details

This function is used internally in dsa()

Author(s)

Daniel Ollech

Examples

a <- daily_sim(n=8)$original
## Not run: make_cal(holidays="Easter", original=a, original2=xts2ts(a, freq=365))

Creating set of dummy variables for specified Holidays

Description

Creating set of dummy variables for specified Holidays

Usage

make_dummy(
  holidays = NULL,
  from = -5,
  to = 5,
  h = 365,
  original = NA,
  original2 = NA
)

Arguments

Details

This function is used internally in dsa()

Author(s)

Daniel Ollech

Creating Holiday dummy

Description

This function uses the Holiday dates of the timeDate::timeDate package to create dummies on a specified holiday.

Usage

make_holiday(dates = timeDate::Easter(2000:2030), shift = 0)

Arguments

Details

With shift the user can specify for how many days before (negative value) or after (positive value) the holiday a dummy will be created.

Author(s)

Daniel Ollech

Examples

make_holiday(dates=timeDate::Easter(2000:2030), shift=-1)

Change multiple xts to a multivariate ts

Description

Change multiple xts to a multivariate ts

Usage

multi_xts2ts(x, short = FALSE)

Arguments

Details

If the ts are used for forecasting

Author(s)

Daniel Ollech

Examples

x <- dsa::daily_sim()$original
y <- dsa::daily_sim()$original
multi_xts2ts(merge(x,y))

Creating Output for dsa

Description

This function creates HTML output in a specified folder for objects of class daily

Usage

output(
  daily_object,
  path = getwd(),
  short = FALSE,
  SI = TRUE,
  SI365.seed = 3,
  spec = TRUE,
  outlier = TRUE,
  Factor = "auto",
  every_day = TRUE,
  seasonals = FALSE,
  spectrum_linesize = 0.5,
  seasonality_tests = TRUE,
  progress_bar = TRUE
)

Arguments

Details

This function can be used to create plots and tables necessary for the analysis of seasonally and calendar adjusted daily time series. Uses the output of dsa() as an input.

Author(s)

Daniel Ollech

Examples

res <- dsa(daily_sim(4)$original, cval=7, model=c(3,1,0),fourier_number = 13)
## Not run: output(res)

Plot daily time series

Description

Plotting output for objects of class "daily"

Usage

## S3 method for class 'daily'
plot(x, dy = TRUE, trend = FALSE, ...)

Arguments

Details

The original series is plotted in black, the seasonally adjusted series is colored in red, and if trend=T, a blue trend line is added.

Author(s)

Daniel Ollech

Examples

x <- daily_sim(3)$original
## Not run: res<- dsa(x, fourier_number = 24, outlier.types="AO", reg.create=NULL, model=c(3,1,0))
## Not run: plot(res, dy=FALSE)

Plot the periodogram of a daily time series

Description

Plot the periodogram of a daily time series

Usage

plot_spectrum(
  x,
  xlog = FALSE,
  size = 1,
  color = "black",
  vline_color = "#6F87B2"
)

Arguments

Details

Plot uses ggplot2 and can be changed accordingly. The spectrum is build around the spec.pgram() function

Author(s)

Daniel Ollech

Examples

x <- daily_sim(3)$original
plot_spectrum(x)

Print daily time series

Description

Print output for objects of class "daily"

Usage

## S3 method for class 'daily'
print(x, ...)

Arguments

Author(s)

Daniel Ollech

Examples

x <- daily_sim(3)$original
## Not run: res<- dsa(x, fourier_number = 24, outlier.types="AO", reg.create=NULL, model=c(3,1,0))
## Not run: print(res)

Change a daily to a weekly differenced time series

Description

This function computes the weekly aggregates or differences (by default Friday to Friday) for any daily time series in the xts format.

Usage

to_weekly(x, incl_forecast = T, forecast_length = 365, diff = T, dayofweek = 5)

Arguments

Author(s)

Daniel Ollech

Examples

to_weekly(xts::xts(rnorm(365, 10,1), seq.Date(as.Date("2010-01-01"), length.out=365, by="days")))

Change ts to xts

Description

Change the format of a time series from ts to xts. Has been optimised for the use in dsa(), i.e. for daily time series.

Usage

ts2xts(x_ts)

Arguments

Details

This function is used internally in dsa(). Does not create values for the 29th of February.

Author(s)

Daniel Ollech

Examples

ts2xts(stats::ts(rnorm(1000, 10,1), start=c(2001,1), freq=365))

Add time series

Description

Sequentially add a set of time series

Usage

ts_sum(...)

Arguments

Details

This function is used internally in dsa()

Author(s)

Daniel Ollech

Examples

ts_sum(list(ts(rnorm(100,10,1)), ts(rnorm(100,10,1)), ts(rnorm(100,10,1))))

Change xts to ts

Description

Change the format of a time series from xts to ts. Has been optimised for the use in dsa(), i.e. for daily time series.

Usage

xts2ts(series, freq = NULL)

Arguments

Details

This function is used internally in dsa(). Does not create values for the 29th of February.

Author(s)

Daniel Ollech

Examples

xts2ts(xts::xts(rnorm(1095, 10,1), seq.Date(as.Date("2010-01-01"), length.out=1095, by="days")))

Create a plot for xts series

Description

Creates a plot using an xts series

Usage

xtsplot(
  xts,
  transform = "none",
  type = "line",
  years = NA,
  scale = 1,
  names = NA,
  color = NA,
  main = "",
  legend = NA,
  textsize = 1,
  textsize_x = NA,
  textsize_y = NA,
  textsize_legend = NA,
  textsize_title = NA,
  linesize = 1.1,
  WeekOfYear = F,
  date_breaks = NA,
  date_labels = NA,
  submain = NULL
)

Arguments

Details

This function uses the ggplot2 package. The difference between type="bar" and type="bar2" is that the former produces barcharts with bars of the second series in front of the bars of the first series (and accordingly for more than two series), while "bar2" creates side-by-side barcharts. If a scale is supplied, the data will be divided by this number.

Author(s)

Daniel Ollech

Examples

x <- xts::xts(rnorm(100), seq.Date(as.Date("2010-01-01"), length.out=100, by="months"))
y <- xts::xts(runif(100), seq.Date(as.Date("2010-01-01"), length.out=100, by="months"))
xtsplot(y, transform="diff", type="bar")
xtsplot(y, transform="diff", type="bar", date_breaks="24 months")
xtsplot(merge(x,y), names=c("Gaussian", "Uniform"), main="Simulated series")