MSBVAR (version 0.9-2)

simulateMSVAR: Simulate a Markov-switching VAR (MSVAR) process

Description

Simulate Markov-switching vector autoregression data

Usage

simulateMSVAR(bigt, m, p, var.beta0, var.betas, e.vcv, Q, seed = 214)

Arguments

bigt

Integer, number of observations to generate.

m

Integer, number of equations in the VAR process

p

Integer, lag length of the VAR(p) process.

var.beta0

Array of dimension $m x 1 x h$ of the VAR intercepts for each regime (h)

var.betas

Array of dimension $m x mp x h$ of the autoregressive coefficients. In each element of the array, rows correspond to equations, columns to lags. The first $m x m$ columns are the AR(1) coefficients, etc.

e.vcv

Array of dimentsion $ m x m x h$ of the error covariances. The $ m x m$ matrices are the error covariances for each regime.

Q

$ h$ dimensional transition matrix for the MS process. $h x h$ Markov transition matrix whose rows sum to 1 with the main weights on the diagonal elements.

seed

Integer. Random number seed.

Value

A list with two elements:

Y

The simulated MSVAR time series in a ts object of dimension $ bigt x m$.

st

A vector of integers identifying the regime of each observation in Y

Details

This function simulates a multivariate Markov-switching model, MSVAR with $m$ equations, $p$ lags and $h$ regimes. The assumption is that the error process is Gaussian.

References

Kim, Chang-Jin and Charles R. Nelson. 1999. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. Cambridge: MIT Press.

See Also

simulateMSAR for the univariate version; msbvar

Examples

## Not run: 
# # Example: simulate an MS(h)-VAR(p) model with two equations.
# # Have h = 2, m=2, and p=1, simplest case
# 
# # VAR simulation parameters
# bigt <- 500  # number of observations
# m <- 2  # number of endogenous variables
# p <- 1  # lag length
# h <- 2  # number of regimes
# 
# # setup transition matrix with two states
# 
# Q <- matrix(c(.98, .02,
#               .05, .95), nrow=h, byrow=TRUE)
# 
# # theta stores paramater values
# # 1st column is intercept
# # 2:m*p are the AR coefficients
# # (mp+2)'th columns are variance
# 
# # regime 1
# var.beta0.st1  <- c(1,2)  # intercepts
# var.betas.st1  <- matrix(c(.7, .1,
#                            .1, .7), m, byrow=TRUE)
# # regime 2
# var.beta0.st2  <- c(0,0)  # intercepts
# var.betas.st2  <- matrix(c(.2, .1,
#                            .2, .1), m, byrow=TRUE)
# 
# # Build the array
# var.beta0 <- array(NA, c(m,1,h))
# var.betas <- array(NA, c(m,p*m,h))
# var.beta0[,,1] <- var.beta0.st1
# var.beta0[,,2] <- var.beta0.st2
# var.betas[,,1] <- var.betas.st1
# var.betas[,,2] <- var.betas.st2
# 
# # Variance-Covariance Matrix for
# # MVN distributed disturbances
# # regime 1
# e.vcv.st1  <- matrix(c(.3, .1,
#                        .1, .3), 2)
# # regime 2
# e.vcv.st2  <- matrix(c(.1, .05,
#                        .05, .1), 2)
# # combine
# e.vcv <- array(NA, c(m, m, h))
# e.vcv[,,1] <- e.vcv.st1
# e.vcv[,,2] <- e.vcv.st2
# 
# # hold true values of parameters for easy comparison to estimates
# theta.true.var <- array(NA, c(m, 1+m*p+m, h))
# theta.true.var[,1,] <- var.beta0
# theta.true.var[,2:(1+p*m),] <- var.betas
# theta.true.var[,(1+m*p+1):ncol(theta.true.var),] <- e.vcv
# 
# simdata <- simulateMSVAR(bigt, m, p, var.beta0, var.betas, e.vcv, Q)
# 
# # Plot
# plot(as.ts(simdata[[1]]))
# 
# # Fit a simple model
# 
# model <- msvar(Y=simdata[[1]], p=1, h=2, niterblkopt=50)
# 
# # Plot regime estimates and compare to true simulated values
# par(mfrow=c(2,1))
# plot(ts(model$fp))
# plot(ts(simdata$st))
# ## End(Not run)