The asymptotic covariance matrix of the multivariate serial correlations (Q1382486)

The asymptotic distribution of the serial covariances of a univariate ARMA process can be expressed in terms of the autocovariance function of another ARMA process, whose parameters are obtained from the parameters of the initial process by squarring its autoregressive operator, moving average operator and the residual variance. Analogous statements are proved for the multivariate case, provided that the square of a matrix \(a\) is interpreted as \(a\otimes a\) (Kronecker (tensor) square of \(a\)). The introduced tensor convolution is of some interest of its own.