simtar function

Simulation of multivariate time series according to a TAR model

This function simulates multivariate time series according to a user-specified TAR model.

simtar(
  n,
  k = 2,
  ars = list(p = 1),
  Intercept = TRUE,
  parms,
  delay = 0,
  thresholds = 0,
  t.series,
  ex.series,
  dist = "gaussian",
  extra
)

Arguments

• n: a positive integer value indicating the length of the desired output series.
• k: a positive integer value indicating the dimension of the desired output series.
• ars: a list composed of three objects, namely: p, q and d, each of which corresponds to a vector of $l$ non-negative integers, where $l$ represents the number of regimes in the TAR model.
• Intercept: an (optional) logical variable. If TRUE, then the model includes an intercept.
• parms: a list with as many sublists as regimes in the user-specified TAR model. Each sublist is composed of two matrices. The first corresponds to location parameters, while the second corresponds to scale parameters.
• delay: an (optional) non-negative integer value indicating the delay in the threshold series.
• thresholds: a vector with $l-1$ real values sorted ascendingly.
• t.series: a matrix with the values of the threshold series.
• ex.series: a matrix with the values of the multivariate exogenous series.
• dist: an (optional) character string which allows the user to specify the multivariate distribution to be used to describe the behavior of the noise process. The available options are: Gaussian ("Gaussian"), Student-$t$ ("Student-t"), Slash ("Slash"), Symmetric Hyperbolic ("Hyperbolic"), Laplace ("Laplace"), and contaminated normal ("Contaminated normal"). As default, dist is set to "Gaussian".
• extra: a value indicating the value of the extra parameter of the noise process distribution, if any.

Returns

a data.frame containing the output series, threshold series (if any), and multivariate exogenous series (if any).

Examples

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

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