tvReg: Time-Varying Coefficient for Single and Multi-Equation Regressions

Description

This package covers a large range of semiparametric regression methods with time-varying coefficients using nonparametric kernel smoothing for the estimation.

Main functions

The five basic functions in this package are tvLM, tvAR, tvSURE, tvPLM, tvVAR and tvIRF. Moreover, this package provides the confint, fitted, forecast, plot, predict, print, resid and summary methods adapted to the class attributes of the tvReg. In addition, it includes bandwidth selection methods, time-varying variance-covariance estimators and four estimation procedures: the time-varying ordinary least squares, which are implemented in the tvOLS methods, the time-varying generalised least squares for a list of equations, which is implemented in the tvGLS methods, time-varying pooled and random effects estimators for panel data, which are implemented in the tvRE and the time-varying fixed effects estimator, which is implemente in the tvFE.

Further information

Details on the theory and applications to finance and macroeconomics can be found in Casas and Fernandez-Casal (2019, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3363526), and in the package vignette https://icasas.github.io/tvReg/articles/tvReg.html.

Acknowledgments

Funded by the Horizon 2020. Framework Programme of the European Union.

Author(s)

Isabel Casas (casasis@gmail.com), Ruben Fernandez-Casal (rubenfcasal@gmail.com).

References

Casas, I. and Fernandez-Casal, R., tvReg: Time-varying Coefficient Linear Regression for Single and Multi-Equations in R (April 1, 2019). Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3363526.

tvReg internal and secondary functions

Description

Listed below are supporting functions for the major methods in tvReg.

Create a list of control pararameters for the tvSURE and tvPLM methods. All control parameters that are not passed to this function are set to default values.

Usage

.tvLM.ci(x, yboot)

.tvSURE.ci(x, yboot)

.kernel(x, bw, tkernel = "Triweight")

.univariatePlot(x, vars = NULL, ylim = NULL, ...)

.tvCov.cv(
  bw,
  x,
  z = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

.tvFE.cv(
  bw,
  x,
  y,
  z = NULL,
  neq,
  obs,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

.tvIRF(
  x,
  impulse,
  response,
  y.names,
  n.ahead,
  ortho,
  ortho.cov,
  bw.cov,
  cumulative
)

.tvOLS.cv(
  bw,
  x,
  y,
  z = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE
)

.tvRE.cv(
  bw,
  x,
  y,
  z = NULL,
  neq,
  obs,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

tvreg.control(maxiter = 100, tol = 1e-05)

Arguments

Details

.kernel calculates the kernel values of a vector and a given bandwidth

If the estimation is iterative FGLS with maxiter>1, the convergence criterion is

\sqrt{ \frac{ \sum_{i, j} (B_{i,j,g} - B{i, j, g-1})^2 }{ \sum_{i, j} B_{i, j, g-1}^2 }} < \code{tol}

(B_{i, j,g} is the ith, jth coefficient of the gth iteration step).

Value

A numeric vector.

A scalar with the mean squared error.

A list of the above components.

Standarised rates from a currency portfolio.

Description

Aslanidis and Casas (2013) consider a portfolio of daily US dollar exchange rates of the Australian dollar (AUS), Swiss franc (CHF), euro (EUR), British pound (GBP), South African rand (RAND), Brazilian real (REALB), and Japanese yen (YEN) over the period from January 1, 1999 until May 7, 2010 (T = 2856 observations). This dataset contains the standarised rates after "devolatilisation", i.e. standarising the rates using a GARCH(1,1) estimate of the volatility.

Format

A data frame with 2855 rows and 8 variables. Below the standarised rates of daily US dollar exchange rates of

Date

Daily data from Jan 6, 1999 until May 7, 2010 - without weekends and days off

AUS

Australian dollar

CHF

Swiss franc

EUR

Euro

GBP

British pound

RAND

South African rand

REALB

Brazilian real

YEN

Japanese yen

References

Aslanidis, N. and Casas, I. (2013) Nonparametric correlation models for portfolio allocation, Journal of Banking and Finance, 37, 2268 - 2283.

Fama and French portfolio daily returns and factors for international markets.

Description

A dataset containing the returns of four portfolios ordered by size and book-to-market. The four portfolios are SMALL/LoBM, SMALL/HiBM, BIG/LoBM and BIG/HiBM in four international markets: North America (NA), Japan (JP), Asia Pacific (AP) and Europe (EU). It also contains the Fama/French 5 factors for each of the markets.

Format

A data frame with 314 rows and 41 variables.

Date

Date, months from July 1990 until August 2016

NA.SMALL.LoBM

Monthly returns of portfolio SMALL/LoBM in North American market

NA.SMALL.HiBM

Monthly returns of portfolio SMALL/HiBM in North American market

NA.BIG.LoBM

Monthly returns of portfolio BIG/LoBM in North American market

NA.BIG.HiBM

Monthly returns of portfolio BIG/HiBM in North American market

NA.Mkt.RF

North American market excess returns, i.e return of the market - market risk free rate

NA.SMB

SMB (Small Minus Big) for the North American market

NA.HML

HML (High Minus Low) for the North American market

NA.RMW

RMW (Robust Minus Weak) for the North American market

NA.CMA

CMA (Conservative Minus Aggressive) for the North American market

NA.RF

North American risk free rate

JP.SMALL.LoBM

Monthly returns of portfolio SMALL/LoBM in Japanese market

JP.SMALL.HiBM

Monthly returns of portfolio SMALL/HiBM in Japanese market

JP.BIG.LoBM

Monthly returns of portfolio BIG/LoBM in Japanese market

JP.BIG.HiBM

Monthly returns of portfolio BIG/HiBM in Japanese market

JP.Mkt.RF

Japanese market excess returns, i.e return of the market - market risk free rate

JP.SMB

SMB (Small Minus Big) for the Japanese market

JP.HML

HML (High Minus Low) for the Japanese market

JP.RMW

RMW (Robust Minus Weak) for the Japanese market

JP.CMA

CMA (Conservative Minus Aggressive) for the Japanese market

JP.RF

Japanese risk free rate

AP.SMALL.LoBM

Monthly returns of portfolio SMALL/LoBM in Asia Pacific market

AP.SMALL.HiBM

Monthly returns of portfolio SMALL/HiBM in Asia Pacific market

AP.BIG.LoBM

Monthly returns of portfolio BIG/LoBM in Asia Pacific market

AP.BIG.HiBM

Monthly returns of portfolio BIG/HiBM in Asia Pacific market

AP.Mkt.RF

Asia Pacific market excess returns, i.e return of the market - maket risk free rate

AP.SMB

SMB (Small Minus Big) for the Asia Pacific market

AP.HML

HML (High Minus Low) for the Asia Pacific market

AP.RMW

RMW (Robust Minus Weak) for the Asia Pacific market

AP.CMA

CMA (Conservative Minus Aggressive) for the Asia Pacific market

AP.RF

Asia Pacific risk free rate

EU.SMALL.LoBM

Excess return of portfolio SMALL/LoBM in European market

EU.SMALL.HiBM

Excess return of portfolio SMALL/HiBM in European market

EU.BIG.LoBM

Excess return of portfolio BIG/LoBM in European market

EU.BIG.HiBM

Excess return of portfolio BIG/HiBM in European market

EU.Mkt.RF

European market excess returns, i.e returns of the market - market risk free rate

EU.SMB

SMB (Small Minus Big) for the European market

EU.HML

HML (High Minus Low) for the European market

EU.RMW

RMW (Robust Minus Weak) for the European market

EU.CMA

CMA (Conservative Minus Aggressive) for the European market

EU.RF

European risk free rate

Source

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

References

Kennet R. French - Data Library (2017) http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#International

Fama, E. and French, K. R (1993) Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 3-56.

Fama, E. F. and French, K. R (2015) A five-factor asset pricing model, Journal of Financial Economics, 116, 1-22.

Variables related to the problem of healthcare spending.

Description

Variables related to the problem of healthcare spending.

Format

A data frame with 680 rows and 7 columns.

country

year

lhe

Log of country's healthcare spending

lgdp

log of country's gdp

pop65

Country's ratio of population greater than 65 years old

pop14

Country's ratio of population younger than 15 years old

public

Country's ratio of healthcare funding coming from the government

References

Casas, I., Gao, J., Peng, B. and Xie, S. (2021). Time-Varying Income Elasticities of Healthcare Expenditure for the OECD and Eurozone. Journal of Applied Econometrics, 36, pp. 328-345.

Daily realized variance

Description

A dataset containing the daily realized variance, and some of its lags, obtained from 1-minute close prices of the SP 500. Similar data has been used in the HAR model in Corsi (2009), the HARQ and SHARQ models in Bollerslev et al (2016) and the TVHARQ and TVSHARQ models in Casas et al (2018). The time period runs from Feb 1990 until Dec 2006.

Format

A data frame with 4264 rows and 6 variables.

Date

Daily data from Feb 1, 1990 until Dec 29, 2006 - without weekends and days off

RV

Daily realized variance at time t

RV_lag

Daily realized variance at time t-1

RV_week

Weekly average realized variance at time t-5

RV_month

Monthly average realized variance at time t-22

RQ_lag_sqrt

Daily squared root of the realized quarticity at time t-1

References

Bollerslev, T., Patton, A. J. and Quaedvlieg, R. (2016) Exploiting the errors: A simple approach for improved volatility forecasting. Journal of Econometrics, 192, 1-18.

Bollerslev, T., Tauchen, G. and Zhou, H. (2009) Expected stock returns and variance risk premia. The Review of Financial Studies, 22, 44-63.

Casas, I., Mao, X. and Vega, H. (2018) Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium. Url= http://pure.au.dk/portal/files/123066669/rp18_10.pdf

Corsi, F. (2009) A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 7, 174-196.

Bandwidth Selection by Cross-Validation

Description

Calculate bandwidth(s) by cross-validation for functions tvSURE, tvVAR and tvLM.

Usage

bw(x, ...)

## Default S3 method:
bw(
  x,
  y,
  z = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE,
  ...
)

## S3 method for class 'list'
bw(
  x,
  y,
  z = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE,
  ...
)

## S3 method for class 'tvlm'
bw(x, ...)

## S3 method for class 'tvar'
bw(x, ...)

## S3 method for class 'tvvar'
bw(x, ...)

## S3 method for class 'tvsure'
bw(x, ...)

## S3 method for class 'tvplm'
bw(x, ...)

## S3 method for class 'pdata.frame'
bw(
  x,
  z = NULL,
  method,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  ...
)

Arguments

Value

bw returns a vector or a scalar with the bandwith to estimate the mean or the covariance residuals, fitted values.

A scalar or a vector of scalars.

A scalar.

Examples

##Generate data
tau <- seq(1:200)/200
beta <- data.frame(beta1 = sin(2*pi*tau), beta2 =  2*tau)
X <- data.frame(X1 = rnorm(200), X2 =  rchisq(200, df = 4))
error <- rt(200, df = 10)
y <- apply(X*beta, 1, sum) + error

##Select bandwidth by cross-validation
bw <- bw(X, y, est = "ll", tkernel = "Gaussian")

data( Kmenta, package = "systemfit" )

## x is a list of matrices containing the regressors, one matrix for each equation
x <- list()
x[[1]] <- Kmenta[, c("price", "income")]
x[[2]] <- Kmenta[, c("price", "farmPrice", "trend")]

## 'y' is a matrix with one column for each equation
y <- cbind(Kmenta$consump, Kmenta$consump)

## Select bandwidth by cross-validation
bw <- bw(x = x, y = y)

##One bandwidth per equation
print(bw)

Covariance Bandwidth Calculation by Cross-Validation bwCov calculates a single bandwidth to estimate the time-varying variance- covariance matrix.

Description

Covariance Bandwidth Calculation by Cross-Validation bwCov calculates a single bandwidth to estimate the time-varying variance- covariance matrix.

Usage

bwCov(
  x,
  z = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

Arguments

Value

A scalar.

Examples

data(CEES)
## Using a shorter set for a quick example. Variable "Date" is removed.
mydata <- tail (CEES[, -1], 50)
bw.cov <- bwCov(mydata)
Sigma.hat <- tvCov(mydata, bw = bw.cov)

Confidence Intervals for Objects in tvReg

Description

confint is used to estimate the bootstrap confidence intervals for objects with class attribute tvlm, tvar, tvirf, tvsure and tvplm.

Usage

## S3 method for class 'tvlm'
confint(
  object,
  parm,
  level = 0.95,
  runs = 100,
  tboot = c("wild", "wild2"),
  ...
)

## S3 method for class 'tvar'
confint(
  object,
  parm,
  level = 0.95,
  runs = 100,
  tboot = c("wild", "wild2"),
  ...
)

## S3 method for class 'tvsure'
confint(
  object,
  parm,
  level = 0.95,
  runs = 100,
  tboot = c("wild", "wild2"),
  ...
)

## S3 method for class 'tvvar'
confint(
  object,
  parm,
  level = 0.95,
  runs = 100,
  tboot = c("wild", "wild2"),
  ...
)

## S3 method for class 'tvirf'
confint(
  object,
  parm,
  level = 0.95,
  runs = 100,
  tboot = c("wild", "wild2"),
  ...
)

## S3 method for class 'tvplm'
confint(
  object,
  parm,
  level = 0.95,
  runs = 100,
  tboot = c("wild", "wild2"),
  ...
)

Arguments

Value

an object of class tvsure with BOOT, Lower and Upper different from NULL.

References

Chen, X. B., Gao, J., Li, D., and Silvapulle, P (2017) Nonparametric estimation and forecasting for time-varying coefficient realized volatility models, Journal of Business and Economic Statistics, 36, 88-100.

Mammen, E (1993) Bootstrap and wild bootstrap for high dimensional linear models, Annals of Statistics, 21, 255-285.

See Also

tvLM, tvAR, tvVAR, tvSURE

Examples

## Not run: 
##Calculation of confidence intervals for a TVLM model

##Generation of time-varying coefficients linear model
set.seed(42)
tau <- seq(1:200)/200
beta <- data.frame(beta1 = sin(2*pi*tau), beta2= 2*tau)
X1 <- rnorm(200)
X2 <- rchisq(200, df = 4)
error <- rt(200, df = 10)
y <- apply(cbind(X1, X2)*beta, 1, sum) + error
data <- data.frame(y = y, X1 = X1, X2 = X2)

##Fitting the model and confidence interval calculation
model.tvlm <-  tvLM(y ~ 0 + X1 + X2, data = data, bw = 0.29)
tvci <- confint(model.tvlm, level = 0.95, runs = 20)

##If a second confidence interval on the "same" object is calculated, 
##for example with a different level, the calculation is faster
tvci.80 <- confint(tvci, level = 0.8)

## End(Not run)

Forecast Methods for Objects in tvReg.

Description

forecast calculates the forecast for objects with class attribute tvlm, tvar, tvvar, tvirf, tvsure and tvplm. If the smoothing variable (z) in the model is non-NULL and it is a random variable then use function predict with parameter newz.

Usage

forecast(object, ...)

## S3 method for class 'tvlm'
forecast(object, newdata, n.ahead = 1, winsize = 0, ...)

## S3 method for class 'tvar'
forecast(object, n.ahead = 1, newz = NULL, newexogen = NULL, winsize = 0, ...)

## S3 method for class 'tvvar'
forecast(object, n.ahead = 1, newz = NULL, newexogen = NULL, winsize = 0, ...)

## S3 method for class 'tvsure'
forecast(object, newdata, n.ahead = 1, winsize = 0, ...)

## S3 method for class 'tvplm'
forecast(object, newdata, n.ahead = 1, winsize = 0, ...)

Arguments

Value

An object of class matrix or vector with the same dimensions than the dependent variable of object.

See Also

predict.

Examples

data("RV")
RV2 <- head(RV, 2001)
TVHAR <- tvLM (RV ~ RV_lag + RV_week + RV_month, data = RV2, bw = 20)
newdata <- cbind(RV$RV_lag[2002:2004], RV$RV_week[2002:2004],
              RV$RV_month[2002:2004])
forecast(TVHAR, newdata, n.ahead = 3)


data("RV")
exogen = RV[1:2001, c("RV_week", "RV_month")]
TVHAR2 <- tvAR(RV$RV_lag[1:2001], p = 1, exogen = exogen, bw = 20)
newexogen <- RV[2002:2004, c("RV_week", "RV_month")]
forecast(TVHAR2, n.ahead = 3, newexogen = newexogen)

data(usmacro, package = "bvarsv")
tvVAR.fit <- tvVAR(usmacro, p = 6, type = "const", bw = c(1.8, 20, 20))
forecast(tvVAR.fit, n.ahead = 10)

data("Kmenta", package = "systemfit")
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice 
system <- list(demand = eqDemand, supply = eqSupply)
tvOLS.fit <- tvSURE(system, data = Kmenta, est = "ll", bw = c(1.5, 1.5))
newdata <- data.frame(price = c(90, 100, 103), farmPrice = c(70, 95, 103), 
income = c(82, 94, 115))
forecast(tvOLS.fit, newdata = newdata, n.ahead = 3)
data(OECD)
tvpols <- tvPLM(lhe~lgdp+pop65+pop14+public, index = c("country", "year"), 
data = OECD, method = "pooling", bw =  8.9)
newdata <- OECD[c(7, 9), 4:7]
forecast(tvpols, newdata = newdata, n.ahead = 2)

Plot Methods for Objects in tvReg

Description

Plot methods for objects with class attribute tvlm, tvar, tvvar, tvirf, tvsure or tvplm.

Usage

## S3 method for class 'tvsure'
plot(x, eqs = NULL, vars = NULL, plot.type = c("multiple", "single"), ...)

## S3 method for class 'tvlm'
plot(x, ...)

## S3 method for class 'tvar'
plot(x, ...)

## S3 method for class 'tvplm'
plot(x, ...)

## S3 method for class 'tvvar'
plot(x, ...)

## S3 method for class 'tvirf'
plot(
  x,
  obs.index = NULL,
  impulse = NULL,
  response = NULL,
  plot.type = c("multiple", "single"),
  ...
)

Arguments

See Also

tvLM, tvAR, tvVAR, tvSURE, tvPLM

Predict Methods for Objects in tvReg.

Description

Predict methods for objects with class attribute tvlm, tvar, tvvar, tvirf, tvsure and tvplm. This function needs new values of variables y (response), x (regressors), exogen (exogenous variables, when used), and z (smoothing variable).

Usage

## S3 method for class 'tvlm'
predict(object, newdata, newz, ...)

## S3 method for class 'tvar'
predict(object, newdata, newz, newexogen = NULL, ...)

## S3 method for class 'tvvar'
predict(object, newdata, newz, newexogen = NULL, ...)

## S3 method for class 'tvsure'
predict(object, newdata, newz, ...)

## S3 method for class 'tvplm'
predict(object, newdata, newz, ...)

Arguments

Value

An object of class matrix or vector with the prediction.

See Also

forecast.

Examples

## Example of TVLM prediction with coefficients as 
## functions of the realized quarticity

data("RV")
RV2 <- head(RV, 2001)
z <- RV2$RQ_lag_sqrt
TVHARQ <- tvLM (RV ~ RV_lag + RV_week + RV_month, 
                 z = z, data = RV2, bw = 0.0062)
newdata <- cbind(RV$RV_lag[2002:2004], RV$RV_week[2002:2004],
              RV$RV_month[2002:2004])
newz <- RV$RQ_lag_sqrt[2002:2004]
predict(TVHARQ, newdata, newz)

## Example of TVAR prediction with coefficients as 
## functions of the realized quarticity
data("RV")
RV2 <- head(RV, 2001)
exogen = RV2[, c("RV_week", "RV_month")]
TVHARQ2 <- tvAR (RV2$RV, p = 1, exogen = exogen,  
                      z = RV2[, "RQ_lag_sqrt"], bw = 0.0062)
newylag <- RV$RV[2002:2004]
newz <- RV$RQ_lag_sqrt[2002:2004]
newexogen <- RV[2002:2004, c("RV_week", "RV_month")]
predict(TVHARQ2, newylag,  newz, newexogen = newexogen)
## Example of TVVAR prediction with coefficients as 
## functions of a random ARMA (2,2) process

data(usmacro, package = "bvarsv")
smoothing <- arima.sim(n = NROW(usmacro) + 3, 
list(ar = c(0.8897, -0.4858), ma = c(-0.2279, 0.2488)), 
sd = sqrt(0.1796))
smoothing <- as.numeric(smoothing)
TVVAR.z <- tvVAR(usmacro, p = 6, type = "const", 
               z = smoothing[1:NROW(usmacro)], bw = c(16.3, 16.3, 16.3))
newdata <- data.frame(inf = c(2, 1, 6), une = c(5, 4, 9), tbi = c(1, 2.5, 3))
newz <- c(0, 1.2, -0.2)
predict(TVVAR.z, newdata = newdata, newz = newz)

## Example of TVSURE prediction with coefficients as 
## functions of an ARMA(2,2) process
data("Kmenta", package = "systemfit")
nobs <- NROW (Kmenta)
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice 
system <- list(demand = eqDemand, supply = eqSupply)
smoothing <- arima.sim(n = nobs + 3, 
                       list(ar = c(0.8897, -0.4858), ma = c(-0.2279, 0.2488)), 
                       sd = sqrt(0.1796))
smoothing <- as.numeric(smoothing)
TVOLS.z <- tvSURE(system, data = Kmenta,  
                      z = smoothing[1:nobs],  bw = c(7, 1.8),
                      est = "ll")
newdata <- data.frame(consump = c(95, 100, 102), price = c(90, 100, 103), 
                      farmPrice = c(70, 95, 103), income = c(82, 94, 115))
newz <- tail(smoothing, 3)
predict(TVOLS.z, newdata = newdata, newz = newz)

data(OECD)
z <- runif(length(levels(OECD$year)), 10, 15)
TVPOLS <- tvPLM(lhe~lgdp+pop65+pop14+public, z = z,
index = c("country", "year"), data = OECD,  method ="pooling", bw =  2)
newdata <- cbind(lgdp = c(10, 13), pop65 = c(9, 12), 
pop14 = c(17, 30), public = c(13, 20))  
newz <- runif(2, 10, 15)
predict(TVPOLS, newdata = newdata, newz = newz)

Print results of functions in tvReg

Description

Print some results for objects with class attribute tvlm, tvar, tvvar, tvirf, tvsure and tvplm.

Usage

## S3 method for class 'tvlm'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvar'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvplm'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvsure'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvvar'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvirf'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Details

These functions print a few results from the time-varying estimated coefficients

See Also

plot.tvlm, plot.tvar, plot.tvvar, plot.tvirf,plot.tvsure, plot.tvplm

Print results of functions in tvReg

Description

Print some results for objects with class attribute tvlm, tvar, tvvar, tvirf, tvsure and tvplm.

Usage

## S3 method for class 'tvlm'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvar'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvplm'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvsure'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvvar'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'tvirf'
summary(object, digits = max(3, getOption("digits") - 3), ...)

Arguments

Details

These functions print a few results from the time-varying estimated coefficients

See Also

plot.tvlm, plot.tvvar, plot.tvvar, plot.tvirf,plot.tvsure

Time-Varying Autoregressive Model

Description

tvAR is used to fit an autorregressive model with time varying coefficients.

Usage

tvAR(
  y,
  p = 1,
  z = NULL,
  ez = NULL,
  bw = NULL,
  cv.block = 0,
  type = c("const", "none"),
  exogen = NULL,
  fixed = NULL,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE
)

Arguments

Details

It is a special case of linear model in which the regressors are lags of the dependent variable. If any variable is included in the xreg term, these are added to the regressors matrix. A time-varying coefficients linear regression (with an intercept if type = "const") is fitted.

Value

An object of class tvar with the following components:

References

Cai, Z. (2007) Trending time-varying coefficient time series with serially correlated errors, Journal of Econometrics, 136, pp. 163-188.

Casas, I., Mao, X. and Veiga, H. (2018) Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium. Url= http://pure.au.dk/portal/files/123066669/rp18_10.pdf

Chen, X. B., Gao, J., Li, D., and Silvapulle, P (2017) Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models. Journal of Business and Economic Statistics, 36, 88-100.

Corsi, F. (2009) A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 7, 174-196.

See Also

bw, tvLM, confint, plot, print and summary

Examples

## Estimate coefficients of different realized variance models
data("RV")
RV2 <- head(RV, 2000)
RV <- RV2$RV
RV_week <- RV2$RV_week
RV_month <- RV2$RV_month
RQ <- RV2$RQ_lag_sqrt
##Corsi (2009) HAR model
HAR <- arima(RV, order = c(1, 0, 0), xreg = cbind (RV_week, RV_month))
print(HAR)

##Chen et al (2017) TVCHAR model 
TVCHAR <- tvAR (RV, p = 1, exogen = cbind (RV_week, RV_month), bw = 20)
print(TVCHAR)

##Casas et al (2018) TVHARQ model
TVHARQ <- tvAR (RV, p = 1, exogen = cbind (RV_week, RV_month), 
z=RQ, bw = 0.0062)
print(TVHARQ)

Time-Varying Coefficient Arrays of the Lagged Endogenous Variables of a TVVAR (no intercept).

Description

Returns the estimated coefficients of the lagged endogenous variables as an array. Given an estimated time varying VAR of the form:

\hat{\bold{y}}_t = \hat{A}_{1t} \bold{y}_{t-1} + \ldots + \hat{A}_{pt} \bold{y}_{t-p} + \hat{C}_tD_t

the function returns a list for each equation with \hat{A}_{1t} | \ldots | \hat{A}_{pt} | \hat{C}_t) set of arrays

Usage

tvAcoef(x)

Arguments

Value

A list object with coefficient arrays for the lagged endogenous variables.

Examples

data(Canada, package="vars")
var.2p <- vars::VAR(Canada, p = 2, type = "const")
tvvar.2p <- tvVAR(Canada, p = 2, type = "const")
A <- vars::Acoef(var.2p)
tvA <- tvAcoef(tvvar.2p)

Coefficient Array of an Estimated tvVAR

Description

Returns the system estimated coefficients as an array.

Usage

tvBcoef(x)

Arguments

Details

Given an estimated time varying VAR of the form:

\hat{{y}}_t = \hat{A}_{1t} {y}_{t-1} + \ldots + \hat{A}_{pt} {y}_{t-p} + \hat{C}_tD_t

the function returns a list for each equation with (\hat{A}_{1t} | \ldots | \hat{A}_{pt} | \hat{C}_t ) set of arrays .

Value

A list object with coefficient arrays for the lagged endogenous variables without including the intercept.

Examples

data(Canada, package="vars")
var.2p <- vars::VAR(Canada, p = 2, type = "const")
tvvar.2p <- tvVAR(Canada, p=2, type= "const")
B <- vars::Bcoef(var.2p)
tvB <- tvBcoef(tvvar.2p)

Time-varying Correlation Estimation

Description

Estimation of a time-varying/functional coefficients correlation matrix using the local constant or the local linear kernel smoothing methodologies.

Usage

tvCor(
  x,
  z = NULL,
  ez = NULL,
  bw = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

Arguments

Value

A matrix of dimension obs x neq x neq.

See Also

tvCov

Examples

##Generate two independent (uncorrelated series)
y <- cbind(rnorm(100, sd = 4), rnorm(100, sd = 1))

##Estimation variance-variance matrix. If the bandwidth is unknown, it can
##calculated with function bwCov()
Rho.hat <-  tvCor(y, bw = 1.4)

##The first time estimate
print(Rho.hat[,,1])
##The mean over time of all estimates
print(apply(Rho.hat, 1:2, mean))
##Generate two dependent variables
y <- MASS::mvrnorm(n = 100, mu = c(0,0), Sigma = cbind(c(1, -0.5), c(-0.5, 4)))

##Estimation variance-variance matrix
Rho.hat <-  tvCor(y, bw = 3.2)
##The first time estimate
print(Rho.hat[,,1])

Time-varying Variance-Covariance Estimation

Description

Estimation of a time-varying/funcional coefficients variance-covariance matrix using the local constant or the local linear kernel smoothing methodologies.

Usage

tvCov(
  x,
  z = NULL,
  ez = NULL,
  bw = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

Arguments

Value

A matrix of dimension obs x neq x neq.

References

Aslanidis, N. and Casas, I (2013) Nonparametric correlation models for portfolio allocation. Journal of Banking and Finance, 37, 2268-2283

See Also

bwCov

Examples

##Generate two independent (uncorrelated series)
y <- cbind(rnorm(100, sd = 4), rnorm(100, sd = 1))

##Estimation variance-variance matrix. If the bandwidth is unknown, it can
##calculated with function bwCov()
Sigma.hat <-  tvCov(y, bw = 1.4)

##The first time estimate
print(Sigma.hat[,,1])
##The mean over time of all estimates
print(apply(Sigma.hat, 1:2, mean))
##Generate two dependent variables
y <- MASS::mvrnorm(n = 100, mu = c(0,0), Sigma = cbind(c(1, -0.5), c(-0.5, 4)))

##Estimation variance-variance matrix
Sigma.hat <-  tvCov(y, bw = 3.2)
##The first time estimate
print(Sigma.hat[,,1])

Time-Varying Fixed Effects Estimation

Description

tvFE estimate time-varying coefficient of fixed effects panel data models using kernel smoothing.

Usage

tvFE(x, ...)

## S3 method for class 'matrix'
tvFE(
  x,
  y,
  z = NULL,
  ez = NULL,
  bw,
  neq,
  obs,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  ...
)

## S3 method for class 'tvplm'
tvFE(x, ...)

Arguments

Value

tvFE returns a list containing:

Time-Varying Generalised Least Squares

Description

tvGLS estimates time-varying coefficients of SURE using the kernel smoothing GLS.

tvGLS is used to estimate time-varying coefficients SURE using the kernel smoothing generalised least square.

Usage

tvGLS(x, ...)

## S3 method for class 'list'
tvGLS(
  x,
  y,
  z = NULL,
  ez = NULL,
  bw,
  Sigma = NULL,
  R = NULL,
  r = NULL,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  ...
)

## S3 method for class 'matrix'
tvGLS(
  x,
  y,
  z = NULL,
  ez = NULL,
  bw,
  Sigma = NULL,
  R = NULL,
  r = NULL,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  ...
)

## S3 method for class 'tvsure'
tvGLS(x, ...)

Arguments

Details

The classical GLS estimator must be modified to generate a set of coefficients changing over time. The tvGLS finds a GLS estimate at a given point in time t using the data near by. The size of the data window used is given by the bandwidth. The closest a point is to t, the larger is its effect on the estimation which is given by the kernel. In this programme, the three possible kernels are the Triweight, Epanechnikov and Gaussian. As in the classical GLS, the covariance matrix is involved in the estimation formula. If this matrix is NULL or the identity, then the program returns the OLS estimates for time-varying coefficients.

Note, that unless with the tvSURE, the tvGLS may run with one common bandwidth for all equations or with a different bandwidths for each equation.

Value

tvGLS returns a list containing:

Examples

data(FF5F)
x <- list()
## SMALL/LoBM porfolios time-varying three factor model
x[[1]] <- cbind(rep (1, 314), FF5F[, c("NA.Mkt.RF", "NA.SMB",  "NA.HML", "NA.RMW", "NA.CMA")])
x[[2]] <- cbind(rep (1, 314), FF5F[, c("JP.Mkt.RF", "JP.SMB",  "JP.HML", "JP.RMW", "JP.CMA")])
x[[3]] <- cbind(rep (1, 314), FF5F[, c("AP.Mkt.RF", "AP.SMB",  "AP.HML", "AP.RMW", "AP.CMA")])
x[[4]] <- cbind(rep (1, 314), FF5F[, c("EU.Mkt.RF", "EU.SMB",  "EU.HML", "EU.RMW", "EU.CMA")])
##Returns
y <- cbind(FF5F$NA.SMALL.LoBM, FF5F$JP.SMALL.LoBM, FF5F$AP.SMALL.LoBM, 
FF5F$EU.SMALL.LoBM) 
##Excess returns
y <- y - cbind(FF5F$NA.RF, FF5F$JP.RF, FF5F$AP.RF, FF5F$EU.RF)
##I fit the data with one bandwidth for each equation
FF5F.fit <- tvGLS(x = x, y = y, bw = c(1.03, 0.44, 0.69, 0.31))

Time-Varying Impulse Response Function

Description

Computes the time-varying impulse response coefficients of an object of class tvvar, obtained with function tvVAR for n.ahead steps.

Usage

tvIRF(
  x,
  impulse = NULL,
  response = NULL,
  n.ahead = 10,
  ortho = TRUE,
  ortho.cov = c("tv", "const"),
  bw.cov = NULL,
  cumulative = FALSE,
  ...
)

Arguments

Value

tvIRF returns and object of class tvirf with the following components:

.

See Also

bw, tvVAR, confint, plot, print and summary

Examples

## Not run: 
##Inflation rate, unemployment rate and treasury bill 
##interest rate for the US as in Primiceri (2005). 
data(usmacro, package = "bvarsv")
TVVAR <- tvVAR(usmacro, p = 4, type = "const")

##Estimate a the tvIRF with time-varying covariance function
TVIRF <- tvIRF(TVVAR)

##Cumulative impulse response function
TVIRF2 <- tvIRF(TVVAR, cumulative = TRUE)

## End(Not run)

Time-Varying Coefficients Linear Models

Description

tvLM is used to fit a time-varying coefficients linear model

Usage

tvLM(
  formula,
  z = NULL,
  ez = NULL,
  data,
  bw = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE
)

Arguments

Details

Models for tvLM are specified symbolically using the same formula format than function lm. A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed. A specification of the form first:second indicates the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.

A formula has an implied intercept term. To remove this use either y ~ x - 1 or y ~ 0 + x.

Value

An object of class tvlm The object of class tvlm have the following components:

References

Bollerslev, T., Patton, A. J. and Quaedvlieg, R. (2016) Exploiting the errors: A simple approach for improved volatility forecasting. Journal of Econometrics, 192, 1-18.

Casas, I., Mao, X. and Veiga, H. (2018) Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium. Url= http://pure.au.dk/portal/files/123066669/rp18_10.pdf

See Also

bw, tvAR, confint, plot, print and summary

Examples

## Simulate a linear process with time-varying coefficient
## as functions of scaled time.
set.seed(42)
tau <- seq(1:200)/200
beta <- data.frame(beta1 = sin(2*pi*tau), beta2= 2*tau)
X1 <- rnorm(200)
X2 <- rchisq(200, df = 4)
error <- rt(200, df = 10)
y <- apply(cbind(X1, X2)*beta, 1, sum) + error
data <- data.frame(y = y, X1 = X1, X2 = X2)
## Estimate coefficients with lm and tvLM for comparison

coef.lm <- stats::lm(y ~ 0 + X1 + X2, data = data)$coef
tvlm.fit <- tvLM(y ~ 0 + X1 + X2, data = data, bw = 0.29)

## Estimate coefficients of different realized variance models
data("RV")
RV2 <- head(RV, 2000)
##Bollerslev t al. (2016) HARQ model
HARQ <- with(RV2, lm(RV ~ RV_lag + I(RV_lag * RQ_lag_sqrt) + RV_week + RV_month))

#Casas et al. (2018) TVHARQ model
TVHARQ <- with(RV2, tvLM (RV ~ RV_lag + RV_week + RV_month, z = RQ_lag_sqrt, 
                         bw = 0.0061))
boxplot(data.frame(TVHARQ = TVHARQ$coefficients[,2] * RV2$RV_lag,
                   HARQ = (HARQ$coef[2] + HARQ$coef[3] * RV2$RQ_lag_sqrt)*RV2$RV_lag),
                   main = expression (RV[t-1]), outline = FALSE)
                 

Time-Varying Ordinary Least Squares

Description

tvOLS estimate time-varying coefficient of univariate linear models using the kernel smoothing OLS.

Usage

tvOLS(x, ...)

## S3 method for class 'matrix'
tvOLS(
  x,
  y,
  z = NULL,
  ez = NULL,
  bw,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE,
  ...
)

## S3 method for class 'tvlm'
tvOLS(x, ...)

## S3 method for class 'tvar'
tvOLS(x, ...)

## S3 method for class 'tvvar'
tvOLS(x, ...)

Arguments

Value

tvOLS returns a list containing:

See Also

bw for bandwidth selection, tvLM and tvAR.

Examples

tau <- seq(1:500)/500
beta <- data.frame(beta1 = sin(2*pi*tau), beta2 = 2*tau)
X <- data.frame(X1 = rnorm(500), X2 = rchisq(500, df = 4))
error <- rt(500, df = 10)
y <- apply(X*beta, 1, sum) + error
coef.lm <- stats::lm(y~0+X1+X2, data = X)$coef
coef.tvlm <-  tvOLS(x = as.matrix(X), y = y, bw = 0.1)$coefficients
plot(tau, beta[, 1], type="l", main="", ylab = expression(beta[1]), xlab = expression(tau),
ylim = range(beta[,1], coef.tvlm[, 1]))
abline(h = coef.lm[1], col = 2)
lines(tau, coef.tvlm[, 1], col = 4)
legend("topright", c(expression(beta[1]), "lm", "tvlm"), col = c(1, 2, 4), bty="n", lty = 1)

Time-Varying Coefficients Panel Data Models

Description

Fits a balanced panel data model using the Time-Varying Pooled Ordinary Least Squares, the Time-Varying Random Effects and the Time-Varying Fixed Effects models.

Usage

tvPLM(
  formula,
  z = NULL,
  ez = NULL,
  data,
  index = NULL,
  bw = NULL,
  bw.cov = NULL,
  cv.block = 0,
  method = c("pooling", "random", "within"),
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  control = tvreg.control(...),
  ...
)

Arguments

Details

This function wraps up the kernel smoothing time-varying coefficient pooled, random effects and fixed effects estimators.

Bandwidth selection is of great importance in kernel smoothing methodologies and it is done automatically by cross-validation.

A panel data model consists of "neq" elements in the cross-sectional dimention and "obs" number of time observations for each cross-section. All variables are the same for each equation which have common coefficients.

Value

tvPLM returns a list of the class tvplm containing the results of model, results of the estimation and confidence instervals if chosen. The object of class tvplm have the following components:

References

Casas, I., Gao, J., Peng, B. and Xie, S. (2021). Time-Varying Income Elasticities of Healthcare Expenditure for the OECD and Eurozone. Journal of Applied Econometrics, 36, pp. 328-345.

Sun, Y., Carrol, R.J and Li, D. (2009). Semiparametric Estimation of Fixed-Effects Panel Data Varying Coefficient Models. Advances in Econometrics, 25, pp. 101-129.

See Also

bw, confint, plot, print and summary

Examples

data(OECD)
##TVPOLS estimation of the model
tvpols <- tvPLM(lhe~lgdp+pop65+pop14+public, index = c("country", "year"),
 data = OECD, method ="pooling", bw = 0.3)
## Not run: 
tvfe <- tvPLM(lhe~lgdp+pop65+pop14+public, index = c("country", "year"),
 data = OECD, method ="within", bw = 0.8)
tvre <- tvPLM(lhe~lgdp+pop65+pop14+public, index = c("country", "year"),
 data = OECD, method ="random", bw = 0.3)

## End(Not run)

Time-Varying Coefficient Arrays of the MA Represention

Description

Returns the estimated time-varying coefficient arrays of the moving average representation of a stable tvvar object obtained with function tvVAR.

Usage

tvPhi(x, nstep = 10, ...)

Arguments

Time-Varying Coefficient Arrays of the Orthogonalised MA Represention

Description

Returns the estimated orthogonalised time-varying coefficient arrays of the moving average representation of a stable tvvar object obtained with function tvVAR.

Usage

tvPsi(x, nstep = 10, ortho.cov = "const", bw.cov = NULL, ...)

Arguments

Value

A list with an array of dimensions (obs x neq x neq nstep + 1) holding the estimated time varying coefficients of the moving average representation, and the bandwidth used to estimate the covariance matrix (optional).

Time-Varying Random Effects Estimation

Description

tvRE estimate time-varying coefficient of a random effects panel data model using kernel smoothing.

Usage

tvRE(x, ...)

## S3 method for class 'matrix'
tvRE(
  x,
  y,
  z = NULL,
  ez = NULL,
  bw,
  Sigma = NULL,
  neq,
  obs,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  ...
)

## S3 method for class 'tvplm'
tvRE(x, ...)

Arguments

Value

tvRE returns a list containing:

Time-Varying Seemingly Unrelated Regression Equations Model

Description

Fits a set of balanced linear structural equations using Time-varying Ordinary Least Squares (tvOLS), Time-varying Seemingly Unrelated Regression (tvGLS), when the error variance-covariance matrix is known, or Time-varying Feasible Seemingly Unrelated Regression (tvFGLS), when the error variance-covariance matrix is unknown.

Usage

tvSURE(
  formula,
  z = NULL,
  ez = NULL,
  bw = NULL,
  cv.block = 0,
  data,
  method = c("tvOLS", "tvFGLS", "tvGLS"),
  Sigma = NULL,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  bw.cov = NULL,
  singular.ok = TRUE,
  R = NULL,
  r = NULL,
  control = tvreg.control(...),
  ...
)

Arguments

Details

This function wraps up the kernel smoothing "tvOLS" and "tvGLS" estimators. The former is used when equations are considered independent while the later assumes that the error term is correlated amongst equations. This relation is given in matrix "Sigma" which is used in the estimation. When "Sigma" is known, the estimates are calculated via the "tvGLS", and via the "tvFGLS" when "Sigma" is unknown and must be estimated.

Bandwidth selection is of great importance in kernel smoothing methodologies and it is done automatically by cross-validation. One important aspect in the current packages is that the bandwidth is selected independently for each equation and then the average is taken to use the same bandwidth for each equation. It has been shown in Casas et al. (2017) that using different bandwidths for each equation is in general a bad practice, even for uncorrelated equations. Even though, the user may be able to use different bandwidths calling functions bw and tvGLS separatedly.

A system consists of "neq" number of equations with "obs" number of observations each and a number of variables not necessarily equal for all equations. The matrix notation is:

Y_{t} = X_t \beta_{t}+u_{t}

where Y_t = (y_{1t}, y_{2t}, \ldots, y_{neq t})', X_t = diag (x_{1t}, x_{2t}, \ldots, x_{neq t}) and \beta_{t} = \left(\beta _{1t}', \ldots, \beta _{neq t}'\right)' is a vector of order the total number of variables in the system. The error vector u_{t} = (u_{1t}, u_{2t}, \ldots, u_{neq t})' has zero mean and covariance matrix E(u_t u_t') = \Sigma_t.

Value

tvSURE returns a list of the class tvsure containing the results of the whole system, results of the estimation and confidence instervals if chosen. The object of class tvsure have the following components:

References

Casas, I., Ferreira, E., and Orbe, S. (2017) Time-Varying Coefficient Estimation in SURE Models: Application to Portfolio Management. Available at SSRN: https://ssrn.com/abstract=3043137

Chen, X. B., Gao, J., Li, D., and Silvapulle, P (2017) Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models. Journal of Business and Economic Statistics, pp.1-13

Granger, C. W (2008) Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models? Studies in Nonlinear Dynamics and Econometrics, 12, pp. 1-11.

Kristensen, D (2012) Non-parametric detection and estimation of structural change. Econometrics Journal, 15, pp. 420-461.

Orbe, S., Ferreira, E., and Rodriguez-Poo, J (2004) On the estimation and testing of time varying constraints in econometric models, Statistica Sinica.

See Also

bw, tvCov, tvVAR, confint, plot, print and summary

Examples

## Not run: 
data("Kmenta", package = "systemfit")
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice + trend
system <- list(demand = eqDemand, supply = eqSupply)
eqSupply2 <- consump ~  price + farmPrice 
system2 <- list(demand = eqDemand, supply = eqSupply2)

##OLS estimation of a system
OLS <- systemfit::systemfit(system, method = "OLS", data = Kmenta)
##tvOLS estimation of a system with the local linear estimator
##removing trend because it is included in the intercept changing over time
TVOLS <- tvSURE(system2, data = Kmenta,  est = "ll")

##SUR/FGLS estimation
FGLS <- systemfit::systemfit(system, data = Kmenta, method = "SUR")
##tvSURE estimation
TVFGLS <- tvSURE(system, data = Kmenta, method = "tvFGLS")

## End(Not run)

Time-varying Vector Autoregressive Models

Description

Fits a time-varying coefficients vector autorregressive model with p lags.

Usage

tvVAR(
  y,
  p = 1,
  z = NULL,
  ez = NULL,
  bw = NULL,
  cv.block = 0,
  type = c("const", "none"),
  exogen = NULL,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE
)

Arguments

Value

An object of class 'tvvar' The object of class tvvar have the following components:

References

Casas, I., Ferreira, E., and Orbe, S. (2017) Time-Varying Coefficient Estimation in SURE Models: Application to Portfolio Management. Available at SSRN: https://ssrn.com/abstract=3043137

Primiceri, G.E. (2005) Time varying structural vector autoregressions and monetary policy. Review of Economic Studies, 72, 821-852.

See Also

bw, tvIRF, plot, print and summary

Examples

##Inflation rate, unemployment rate and treasury bill interest rate for 
##the US, as used in Primiceri (2005).
data(usmacro, package = "bvarsv")
VAR.fit <- vars::VAR(usmacro, p = 6, type = "const")
tvVAR.fit <- tvVAR(usmacro, p = 6, type = "const", bw = c(1.8, 20, 20))
plot(tvVAR.fit)

Update and Re-fit the Models of package tvReg

Description

Update and Re-fit the Models of package tvReg

Usage

## S3 method for class 'tvlm'
update(object, ...)

## S3 method for class 'tvar'
update(object, ...)

## S3 method for class 'tvvar'
update(object, ...)

## S3 method for class 'tvsure'
update(object, ...)

## S3 method for class 'tvplm'
update(object, ...)

Arguments

Value

An object of the same class than the argument *object*.