Compute The Vector of Moving Average Model (VMA)

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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

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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".

See Also

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

Examples

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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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