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.

1 | ```
vma.sim(psi, a)
``` |

`psi` |
the impulse coefficients. |

`a` |
innovations |

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.

Esam Mahdi and A.I. McLeod.

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)
``` |

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