portes (version 6.0)

vma.sim: Compute The Vector of Moving Average Model (VMA)

Description

This utility function is useful to use in the function varima.sim and may used to compute the coefficients of moving-average or vector moving-average.

Usage

vma.sim(psi, a)

Value

Vector of length \(n\) (in the univariate case), or \(n\) matrices (in the multivariate case), where \(n\) = length(\(a\))-length(\(\Psi\)) and \(n\times k\) is the dimension of the series.

Arguments

psi

the impulse coefficients.

a

innovations

Author

Esam Mahdi and A.I. McLeod.

References

Hannan, E.J. (1970). "Multiple Time Series". New York: Wiley.

Hipel, K.W. and McLeod, A.I. (2005). "Time Series Modelling of Water Resources and Environmental Systems".

See Also

convolve, varima.sim, arima.sim, ImpulseVMA, InvertQ

Examples

k <- 2
n <- 300
trunc.lag <-  50   
ar <-  array(c(0.5,0.4,0.1,0.5),dim=c(k,k,1))
ma <-  array(c(0,0.25,0,0),dim=c(k,k,1))
sigma <- matrix(c(1,0.71,0.71,2),k,k)
p <- ifelse(is.null(ar),0,dim(ar)[3])
q <- ifelse(is.null(ma),0,dim(ma)[3])
r <- max(p, q)
d <- trunc.lag + r
psi <- ImpulseVMA(ar = ar, ma = ma, trunc.lag = trunc.lag)
a <- t(crossprod(chol(sigma),matrix(rnorm(k*d),ncol=d)))
vma.sim(psi = psi, a = a)