It is known that the autocorrelation function of a stationary discrete-time scalar process can be uniquely characterized by the so-called partial autocorrelation function, which is a sequence of numbers less or equal to one in magnitude. We show here that the matrix covariance function of a multivariate stationary process can be characterized by a sequence of matrix partial correlations, having singular values less than or equal to one in magnitude. This characterization can be used to extend to the multivariate case the so-called maximum entropy spectral analysis method.
"Covariance Characterization by Partial Autocorrelation Matrices." Ann. Statist. 6 (3) 643 - 648, May, 1978. https://doi.org/10.1214/aos/1176344208