Deviance Information Criterion (DIC)

Description

Computes the Deviance Information Criterion (DIC), an adjusted within-sample measure of predictive accuracy, for models estimated using Bayesian methods.

Usage

DIC(...)

Arguments

Value

A numeric matrix containing the DIC values corresponding to each fitted object supplied in ....

References

Spiegelhalter D.J., Best N.G., Carlin B.P. and Van Der Linde A. (2002) Bayesian Measures of Model Complexity and Fit. Journal of the Royal Statistical Society Series B (Statistical Methodology), 64(4), 583–639.

Spiegelhalter D.J., Best N.G., Carlin B.P. and Van der Linde A. (2014). The deviance information criterion: 12 years on. Journal of the Royal Statistical Society Series B (Statistical Methodology), 76(3), 485–493.

Deviance Information Criterion (DIC) for objects of class mtar

Description

This function computes the Deviance Information Criterion (DIC) for objects of class mtar.

Usage

## S3 method for class 'mtar'
DIC(...)

Arguments

Value

A numeric matrix containing the DIC values corresponding to each mtar object in the input.

See Also

WAIC

Examples

###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1a <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
              subset={Date<="2016-03-14"}, dist="Student-t",
              ars=ars(nregim=3,p=c(1,1,2)), n.burnin=2000, n.sim=3000,
              n.thin=2)
fit1b <- update(fit1a,dist="Slash")
fit1c <- update(fit1a,dist="Laplace")
DIC(fit1a,fit1b,fit1c)

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2a <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
              subset={Date<="2009-04-04"}, dist="Laplace",
              ars=ars(nregim=3,p=5), n.burnin=2000, n.sim=3000, n.thin=2)
fit2b <- update(fit2a,dist="Slash")
fit2c <- update(fit2a,dist="Student-t")
DIC(fit2a,fit2b,fit2c)

###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3a <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
              data=iceland.rf, subset={Date<="1974-12-21"}, row.names=Date,
              ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=2000, n.sim=3000,
              n.thin=2, dist="Slash")
fit3b <- update(fit3a,dist="Laplace")
fit3c <- update(fit3a,dist="Student-t")
DIC(fit3a,fit3b,fit3c)

Highest Posterior Density intervals for objects of class mtar

Description

Highest Posterior Density intervals for objects of class mtar

Usage

## S3 method for class 'mtar'
HPDinterval(obj, prob = 0.95, ...)

Arguments

See Also

HPDinterval

U.S. Stock Returns

Description

The dataset comprises observations of both continuously compounded and simple returns derived from the S&P 500 index, along with the first difference of the Chicago Board Options Exchange Market Volatility Index (VIX). The sample period spans from January 5, 1990, to March 30, 2012.

Usage

data(US.returns)

Format

A data frame with 5606 rows and 4 variables:

Date

A vector indicating the date of each observation.

CCR

A numeric vector giving the continuously compounded returns.

SR

A numeric vector giving the simple returns.

dVIX

A numeric vector giving (the first difference of) the Chicago Board Options Exchange Market Volatility Index (VIX).

References

Massacci, D. (2014) A two-regime threshold model with conditional skewed student-t distributions for stock returns. Economic Modelling, 43, 9-20.

Examples

data(US.returns)
dev.new()
plot(ts(as.matrix(US.returns[,-1])), main="Returns and (the first difference of) VIX")

Watanabe-Akaike or Widely Available Information Criterion (WAIC)

Description

Computes Watanabe-Akaike or Widely Available Information Criterion (WAIC), an adjusted within-sample measure of predictive accuracy, for models estimated using Bayesian methods.

Usage

WAIC(...)

Arguments

Value

A numeric matrix containing the WAIC values corresponding to each fitted object supplied in ....

References

Watanabe S. (2010). Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. The Journal of Machine Learning Research, 11, 3571–3594.

Watanabe-Akaike or Widely Available Information Criterion (WAIC) for objects of class mtar

Description

This function computes the Watanabe-Akaike or Widely Available Information Criterion (WAIC), for objects of class mtar.

Usage

## S3 method for class 'mtar'
WAIC(...)

Arguments

Value

A numeric matrix containing the WAIC values corresponding to each mtar object in the input.

See Also

DIC

Examples

###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1a <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
              subset={Date<="2016-03-14"}, dist="Student-t",
              ars=ars(nregim=3,p=c(1,1,2)), n.burnin=2000, n.sim=3000,
              n.thin=2)
fit1b <- update(fit1a,dist="Slash")
fit1c <- update(fit1a,dist="Laplace")
WAIC(fit1a,fit1b,fit1c)

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2a <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
              subset={Date<="2009-04-04"}, dist="Laplace",
              ars=ars(nregim=3,p=5), n.burnin=2000, n.sim=3000, n.thin=2)
fit2b <- update(fit2a,dist="Slash")
fit2c <- update(fit2a,dist="Student-t")
WAIC(fit2a,fit2b,fit2c)

###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3a <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
              data=iceland.rf, subset={Date<="1974-12-21"}, row.names=Date,
              ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=2000, n.sim=3000,
              n.thin=2, dist="Slash")
fit3b <- update(fit3a,dist="Laplace")
fit3c <- update(fit3a,dist="Student-t")
WAIC(fit3a,fit3b,fit3c)

Auxiliary function to specify the number of regimes and lag orders

Description

This auxiliary function defines the regime structure of a multivariate TAR model by specifying the number of regimes and the corresponding lag orders for the endogenous, exogenous, and threshold series in each regime.

Usage

ars(nregim = 1, p = 1, q = 0, d = 0)

Arguments

Value

A list containing the number of regimes and the regime-specific lag-order specifications.

Coercion of mtar objects to mcmc objects

Description

This method converts an object of class mtar into a list of mcmc objects, each corresponding to a Markov chain produced during Bayesian estimation.

Usage

## S3 method for class 'mtar'
as.mcmc(x, ...)

Arguments

Value

A list of mcmc objects containing the posterior simulation draws generated by the mtar() routine.

See Also

as.mcmc

Examples

###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
             subset={Date<="2016-03-14"}, dist="Student-t",
             ars=ars(nregim=3,p=c(1,1,2)), n.burnin=2000, n.sim=3000,
             n.thin=2)
fit1.mcmc <- coda::as.mcmc(fit1)
summary(fit1.mcmc)

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
             subset={Date<="2009-04-04"}, dist="Laplace",
             ars=ars(nregim=3,p=5), n.burnin=2000, n.sim=3000, n.thin=2)
fit2.mcmc <- coda::as.mcmc(fit2)
summary(fit2.mcmc)

###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3 <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
             data=iceland.rf, subset={Date<="1974-12-21"}, row.names=Date,
             ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=2000, n.sim=3000,
             n.thin=2, dist="Slash")
fit3.mcmc <- coda::as.mcmc(fit3)
summary(fit3.mcmc)

coef method for objects of class mtar

Description

coef method for objects of class mtar

Usage

## S3 method for class 'mtar'
coef(object, ..., FUN = mean)

Arguments

Value

A list containing the summary statistics obtained by applying FUN to the MCMC chains of each model parameter.

Geweke's convergence diagnostic for mtar objects

Description

This function computes Geweke's convergence diagnostic for Markov chain Monte Carlo (MCMC) output obtained from Bayesian estimation of multivariate TAR models. It is a wrapper around geweke.diag() that applies the diagnostic to the posterior chains returned by a call to mtar().

Usage

geweke.diagTAR(x, frac1 = 0.1, frac2 = 0.5)

Arguments

Value

A list containing the Geweke z-scores for the parameters of the mtar model.

See Also

geweke.diag

Geweke-Brooks plot for objects of class mtar

Description

This function is a wrapper around geweke.plot() that applies the Geweke-Brooks convergence diagnostic to the MCMC chains obtained from a fitted mtar model.

Usage

geweke.plotTAR(
  x,
  frac1 = 0.1,
  frac2 = 0.5,
  nbins = 20,
  pvalue = 0.05,
  auto.layout = TRUE,
  ask,
  ...
)

Arguments

See Also

geweke.plot

Temperature, precipitation, and two river flows in Iceland

Description

This data set contains two daily river-flow time series, measured in cubic meters per second, for rivers in Iceland from January 1, 1972, to December 12, 1974. Additionally, daily measurements of precipitation (in millimeters) and temperature (in degrees Celsius) were recorded at the Hveravellir meteorological station. The precipitation values correspond to the accumulated precipitation up to 9:00 A.M. relative to the same time on the previous day.

Usage

data(iceland.rf)

Format

A data frame with 1,096 rows and 5 variables:

Vatnsdalsa

Numeric vector representing the daily flow of the Vatnsdalsá river.

Jokulsa

Numeric vector representing the daily flow of the Jökulsá Eystri river.

Precipitation

Numeric vector of daily precipitation amounts (millimeters).

Temperature

Numeric vector of daily temperature measurements (degrees Celsius).

Date

Vector indicating the calendar date of each observation.

References

Tong, Howell (1990) Non‑linear Time Series: A Dynamical System Approach. Oxford University Press. Oxford, UK.

Ruey S., Tsay (1998) Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93, 1188-1202.

Examples

data(iceland.rf)
dev.new()
plot(ts(as.matrix(iceland.rf[,-5])), main="Iceland")

Bayesian estimation of a multivariate Threshold Autoregressive (TAR) model.

Description

This function implements a Gibbs sampling algorithm to draw samples from the posterior distribution of the parameters of a multivariate Threshold Autoregressive (TAR) model and its special cases as SETAR and VAR models. The procedure accommodates a wide range of noise process distributions, including Gaussian, Student-t, Slash, Symmetric Hyperbolic, Contaminated normal, Laplace, Skew-normal, and Skew-Student-t.

Usage

mtar(
  formula,
  data,
  subset,
  Intercept = TRUE,
  trend = c("none", "linear", "quadratic"),
  nseason = NULL,
  ars = ars(),
  row.names,
  dist = c("Gaussian", "Student-t", "Hyperbolic", "Laplace", "Slash",
    "Contaminated normal", "Skew-Student-t", "Skew-normal"),
  prior = list(),
  n.sim = 500,
  n.burnin = 100,
  n.thin = 1,
  ssvs = FALSE,
  setar = NULL,
  progress = TRUE,
  ...
)

Arguments

Value

an object of class mtar in which the main results of the model fitted to the data are stored, i.e., a list with components including

References

Nieto, F.H. (2005) Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics - Theory and Methods, 34, 905-930.

Romero, L.V. and Calderon, S.A. (2021) Bayesian estimation of a multivariate TAR model when the noise process follows a Student-t distribution. Communications in Statistics - Theory and Methods, 50, 2508-2530.

Calderon, S.A. and Nieto, F.H. (2017) Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46, 296-318.

Vanegas, L.H. and Calderón, S.A. and Rondón, L.M. (2025) Bayesian estimation of a multivariate tar model when the noise process distribution belongs to the class of gaussian variance mixtures. International Journal of Forecasting.

See Also

DIC, WAIC

Examples

###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
             subset={Date<="2016-03-14"}, dist="Student-t",
             ars=ars(nregim=3,p=c(1,1,2)), n.burnin=2000, n.sim=3000,
             n.thin=2, ssvs=TRUE)
summary(fit1)

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
             subset={Date<="2009-04-04"}, dist="Laplace", ssvs=TRUE,
             ars=ars(nregim=3,p=5), n.burnin=2000, n.sim=3000, n.thin=2)
summary(fit2)

###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3 <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
             data=iceland.rf, subset={Date<="1974-12-21"}, row.names=Date,
             ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=2000, n.sim=3000,
             n.thin=2, dist="Slash")
summary(fit3)

Bayesian Estimation of Multivariate TAR Models

Description

This function is a wrapper that applies mtar() over a grid of model specifications defined by all combinations of the noise distribution (dist), the number of regimes (from nregim.min to nregim.max), the autoregressive order within each regime (from p.min to p.max), the maximum lag of the exogenous series within each regime (from q.min to q.max), and the maximum lag of the threshold series within each regime (from d.min to d.max). In all calls to mtar(), the same set of time points is used for model fitting. This is achieved by appropriately adjusting the subset argument of mtar() for each model specification, thereby ensuring comparability across models.

Usage

mtar_grid(
  formula,
  data,
  subset,
  Intercept = TRUE,
  trend = c("none", "linear", "quadratic"),
  nseason = NULL,
  nregim.min = 1,
  nregim.max = NULL,
  p.min = 1,
  p.max = NULL,
  q.min = 0,
  q.max = 0,
  d.min = 0,
  d.max = 0,
  row.names,
  dist = "Gaussian",
  prior = list(),
  n.sim = 500,
  n.burnin = 100,
  n.thin = 1,
  ssvs = FALSE,
  setar = NULL,
  plan_strategy = c("sequential", "multisession"),
  progress = TRUE
)

Arguments

Value

A list whose elements are objects of class mtar, each corresponding to a distinct model specification considered in the grid.

See Also

mtar

Out-of-sample predictive accuracy measures

Description

Computes out-of-sample predictive accuracy measures for one or more fitted models of the same class, based on their predictive distributions.

Usage

out.of.sample(..., newdata, n.ahead)

Arguments

Forecasting for multivariate TAR models

Description

Computes forecasts from a fitted multivariate Threshold Autoregressive (TAR) model.

Usage

## S3 method for class 'mtar'
predict(
  object,
  ...,
  newdata,
  n.ahead = 1,
  row.names,
  credible = 0.95,
  out.of.sample = FALSE
)

Arguments

Value

A list containing the forecast summaries and, when requested, measures of predictive accuracy.

References

Nieto, F.H. (2005) Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics - Theory and Methods, 34, 905-930.

Romero, L.V. and Calderon, S.A. (2021) Bayesian estimation of a multivariate TAR model when the noise process follows a Student-t distribution. Communications in Statistics - Theory and Methods, 50, 2508-2530.

Calderon, S.A. and Nieto, F.H. (2017) Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46, 296-318.

Karlsson, S. (2013) Chapter 15-Forecasting with Bayesian Vector Autoregression. In Elliott, G. and Timmermann, A. Handbook of Economic Forecasting, Volume 2, 791–89, Elsevier.

Vanegas, L.H. and Calderón, S.A. and Rondón, L.M. (2025) Bayesian estimation of a multivariate tar model when the noise process distribution belongs to the class of gaussian variance mixtures. International Journal of Forecasting.

Examples

###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
             subset={Date<="2016-03-14"}, dist="Student-t",
             ars=ars(nregim=3,p=c(1,1,2)), n.burnin=2000, n.sim=3000,
             n.thin=2, ssvs=TRUE)
out1 <- predict(fit1, newdata=subset(returns,Date>"2016-03-14"), n.ahead=10)
out1$summary

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
             subset={Date<="2009-04-04"}, dist="Laplace",
             ars=ars(nregim=3,p=5), n.burnin=2000, n.sim=3000, n.thin=2)
out2 <- predict(fit2, newdata=subset(riverflows,Date>"2009-04-04"), n.ahead=10)
out2$summary

###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3 <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
             data=iceland.rf, subset={Date<="1974-12-21"}, row.names=Date,
             ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=2000, n.sim=3000,
             n.thin=2)
out3 <- predict(fit3, newdata=subset(iceland.rf,Date>"1974-12-21"), n.ahead=10)
out3$summary

Auxiliary function for setting hyperparameter values

Description

This function constructs and validates the list of hyperparameter values used to define the prior distributions of the model parameters. Hyperparameters not explicitly provided by the user are assigned their default values, which define non-informative prior distributions.

Usage

priors(prior, regim, k, dist, setar, ssvs)

Arguments

Value

A list containing the hyperparameter values defining the prior distributions of all model parameters.

Returns of the closing prices of three financial indexes

Description

This dataset contains daily returns computed from the closing prices of the COLCAP, BOVESPA, and S&P 500 stock market indexes over the period from February 10, 2010, to March 31, 2016, comprising 1,505 observations. The COLCAP index reflects the price dynamics of the 20 most liquid stocks traded on the Colombian stock market. The BOVESPA index represents the Brazilian stock market, the largest and most important exchange in Latin America and among the largest worldwide. The Standard & Poor's 500 (S&P 500) index tracks the performance of 500 large-cap companies listed in the United States.

Usage

data(returns)

Format

A data frame with 1,505 rows and 4 variables:

Date

A vector indicating the date of each observation.

COLCAP

A numeric vector containing the returns of the COLCAP index.

SP500

A numeric vector containing the returns of the S&P 500 index.

BOVESPA

A numeric vector containing the returns of the BOVESPA index.

References

Romero, L.V. and Calderon, S.A. (2021) Bayesian estimation of a multivariate TAR model when the noise process follows a Student-t distribution. Communications in Statistics - Theory and Methods, 50, 2508-2530.

Examples

data(returns)
dev.new()
plot(ts(as.matrix(returns[,-1])), main="Returns")

Rainfall and two river flows in Colombia

Description

This dataset contains daily observations of rainfall (in millimeters) and river flows (in m^3/s) for two rivers in southern Colombia. Rainfall was recorded at a meteorological station located at an altitude of 2400 meters above sea level. River flows were measured at two hydrological stations: El Trébol station, which monitors the Bedón River at an altitude of 1720 meters, and Villalosada station, which monitors the La Plata River at an altitude of 1300 meters. The stations are located near the equator, a geographic feature that helps reduce seasonal distortions and facilitates the analysis of the dynamic relationship between rainfall and river flows. The sample period spans from January 1, 2006, to April 14, 2009.

Usage

data(riverflows)

Format

A data frame with 1200 rows and 4 variables:

Date

A vector indicating the date of each observation.

Bedon

A numeric vector giving the daily flow of the Bedón River.

LaPlata

A numeric vector giving the daily flow of the La Plata River.

Rainfall

A numeric vector indicating daily rainfall amounts.

References

Calderon, S.A. and Nieto, F.H. (2017) Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46, 296-318.

Examples

data(riverflows)
dev.new()
plot(ts(as.matrix(riverflows[,-1])), main="Rainfall and river flows")

Simulation of multivariate time series from a TAR model

Description

This function simulates multivariate time series generated by a user-specified Threshold Autoregressive (TAR) model.

Usage

simtar(
  n,
  k = 2,
  ars = ars(),
  Intercept = TRUE,
  trend = c("none", "linear", "quadratic"),
  nseason = NULL,
  parms,
  delay = 0,
  thresholds = NULL,
  t.series = NULL,
  ex.series = NULL,
  dist = c("Gaussian", "Student-t", "Hyperbolic", "Laplace", "Slash",
    "Contaminated normal", "Skew-Student-t", "Skew-normal"),
  skewness = NULL,
  extra = NULL,
  setar = NULL,
  Verbose = TRUE
)

Arguments

Value

A data.frame containing the simulated multivariate output series, and, if specified, the threshold series and multivariate exogenous series.

References

Vanegas, L.H. and Calderón, S.A. and Rondón, L.M. (2025) Bayesian estimation of a multivariate tar model when the noise process distribution belongs to the class of gaussian variance mixtures. International Journal of Forecasting.

Examples

###### Simulation of a trivariate TAR model with two regimes
n <- 2000
k <- 3
myars <- ars(nregim=2,p=c(1,2))
Z <- as.matrix(arima.sim(n=n+max(myars$p),list(ar=c(0.5))))
probs <- sort((0.6 + runif(myars$nregim-1)*0.8)*c(1:(myars$nregim-1))/myars$nregim)
dist <- "Student-t"; extra <- 6
parms <- list()
for(j in 1:myars$nregim){
    np <- 1 + myars$p[j]*k
    parms[[j]] <- list()
    parms[[j]]$location <- c(ifelse(runif(np*k)<=0.5,1,-1)*rbeta(np*k,shape1=4,shape2=16))
    parms[[j]]$location <- matrix(parms[[j]]$location,np,k)
    parms[[j]]$scale <- rgamma(k,shape=1,scale=1)*diag(k)
}
thresholds <- quantile(Z,probs=probs)
out1 <- simtar(n=n, k=k, ars=myars, parms=parms, thresholds=thresholds,
               t.series=Z, dist=dist, extra=extra)
str(out1)

fit1 <- mtar(~ Y1 + Y2 + Y3 | Z, data=out1, ars=myars, dist=dist,
             n.burn=2000, n.sim=3000, n.thin=2)
summary(fit1)

###### Simulation of a trivariate VAR model
n <- 2000
k <- 3
myars <- ars(nregim=1,p=2)
dist <- "Slash"; extra <- 2
parms <- list()
for(j in 1:myars$nregim){
    np <- 1 + myars$p[j]*k
    parms[[j]] <- list()
    parms[[j]]$location <- c(ifelse(runif(np*k)<=0.5,1,-1)*rbeta(np*k,shape1=4,shape2=16))
    parms[[j]]$location <- matrix(parms[[j]]$location,np,k)
    parms[[j]]$scale <- rgamma(k,shape=1,scale=1)*diag(k)
}
out2 <- simtar(n=n, k=k, ars=myars, parms=parms, dist=dist, extra=extra)
str(out2)

fit2 <- mtar(~ Y1 + Y2 + Y3, data=out2, ars=myars, dist=dist,
             n.burn=2000, n.sim=3000, n.thin=2)
summary(fit2)

n <- 5000
k <- 3
myars <- ars(nregim=2,p=c(1,2))
dist <- "Laplace"
parms <- list()
for(j in 1:myars$nregim){
    np <- 1 + myars$p[j]*k
    parms[[j]] <- list()
    parms[[j]]$location <- c(ifelse(runif(np*k)<=0.5,1,-1)*rbeta(np*k,shape1=4,shape2=16))
    parms[[j]]$location <- matrix(parms[[j]]$location,np,k)
    parms[[j]]$scale <- rgamma(k,shape=1,scale=1)*diag(k)
}
out3 <- simtar(n=n, k=k, ars=myars, parms=parms, delay=2,
               thresholds=-1, dist=dist, setar=2)
str(out3)

fit3 <- mtar(~ Y1 + Y2 + Y3, data=out3, ars=myars, dist=dist,
             n.burn=2000, n.sim=3000, n.thin=2, setar=2)
summary(fit3)

vcov method for objects of class mtar

Description

Computes estimates of the variance–covariance matrices for the scale parameters of a fitted multivariate TAR model.

Usage

## S3 method for class 'mtar'
vcov(object, ..., FUN = mean)

Arguments

Value

A list containing the variance–covariance estimates obtained by applying FUN to the MCMC chains associated with the scale parameters.