Multivariate context:

As in the previous model, here again we construct the covariance matrix $\Sigma_t$. The matrix elements are generated with the intuitively obvious bivariate generalization of the univariate case:

 

s_t^(jk) = s_t^(kj) = 0.94s_t-1^(jk) + 0.06x_t^(j)x_t^(k).

Then, using standard multivariate probability theory the forecast distribution p_t^(P) for x_t+1^(P) is constructed from $\Sigma_t$ in the same manner as expressed at the end of section  (expression ).