# 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

 1 vma.sim(psi, a) 

### Arguments

 psi the impulse coefficients. a innovations

### Value

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

### Author(s)

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".

convolve, varima.sim, arima.sim, ImpulseVMA, InvertQ, fitstable
  1 2 3 4 5 6 7 8 9 10 11 12 13 k <- 2 n <- 300 Trunc.Series <- 50 phi <- array(c(0.5,0.4,0.1,0.5),dim=c(k,k,1)) theta <- 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(phi),0,dim(phi)[3]) q <- ifelse(is.null(theta),0,dim(theta)[3]) r <- max(p, q) d <- Trunc.Series + r psi <- ImpulseVMA(phi = phi, theta = theta, Trunc.Series = Trunc.Series) a <- t(crossprod(chol(sigma),matrix(rnorm(k*d),ncol=d))) vma.sim(psi = psi, a = a)