= Multivariate moving-average model
{title2=$Z_t=\sum_{j=0}^q\Theta_jW_{t-j}$}
A multivariate <moving-average model> filters vector <white noise> through fixed matrix coefficients. If the noise has zero <mean> and lag-zero <covariance matrix> $D$, with all nonzero-lag cross-covariances zero, then the filtered process is a <weakly stationary process>. With the convention $\Gamma(h)=\mathbb E[Z_tZ_{t+h}^T]$, its <covariance matrix> is $\Gamma(h)=\sum_j\Theta_jD\Theta_{j+h}^T$, omitting terms outside the filter range. Positive and negative lags satisfy $\Gamma(-h)=\Gamma(h)^T$.
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