VARMASIM Call

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VARMASIM Call

generates a VARMA(p,q) series

CALL VARMASIM( series, phi, theta, mu, sigma, n <, p, q, initial, seed>);

The inputs to the VARMASIM subroutine are as follows:

phi: specifies to a kp ×k matrix containing the vector autoregressive coefficient matrices.
theta: specifies to a kq ×k matrix containing the vector moving-average coefficient matrices. You must specify either phi or theta.
mu: specifies a k ×1 (or 1 ×k) mean vector of the series. By default, mu is a zero vector.
sigma: specifies a k ×k covariance matrix of the innovation series. By default, sigma is an identity matrix with dimension k.
n: specifies the length of the series. By default, n=100.
p: specifies the order of VAR. See the VARMACOV subroutine.
q: specifies the order of VMA. See the VARMACOV subroutine.
initial: specifies the initial values of random variables. If initial=a₀, y_-p+1, ... ,y₀ and $m\epsilon_{-q+1}, ... ,\epsilon_{0}$ take all the same value as initial=a₀. If initial option is not specified, the initial values are estimated using VARMACOV for stationary vector time series, while the initial values assume as zero values for nonstationary vector time series.
seed: specifies the random number seed. See the VNORMAL subroutine.

The VARMASIM subroutine returns the following value:

series: refers an n×k matrices the generated VARMA(p,q) series. When either initial option is specified or the zero initial values are used, the returns do not print these initial values.

To generate a bivariate(k=2) stationary VARMA(1,1) time series

$y_t - m{\mu} = \Phi ( y_{t-1} - m{\mu} ) + m{\epsilon}_t - \Theta m{\epsilon}_{t-1},$

with $m{\epsilon}_t \sim WN( 0, \Sigma)$ ,where

$\Sigma=[\matrix{1.0 & 0.5 \cr 0.5 & 1.25\cr }], \mu=[\matrix{10 \cr 20 \cr}], ... ... -0.5 \cr 0.6 & 0.3 \cr }], \Theta=[\matrix{-0.6 & 0.3 \cr 0.3 & 0.6 \cr }],$

you can specify

  call varmasim(yt, phi, theta, mu, sigma, 100);

To generate a bivariate(k=2) nonstationary VARMA(1,1) time series with the same mu, sigma, and theta in previous example and the AR coefficient

$\Phi=[\matrix{1.0 & 0 \cr 0 & 0.3 \cr }],$

you can specify

  call varmasim(yt, phi, theta, mu, sigma, 100) initial=3;

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