Matrix polynomials orthogonal on the unit circle and accuracy of autoregressive models
Orthogonal matrix polynomials on the unit circle with respect to a positive definite matrix valued measure \(K(\theta)d\theta\) are studied. An upper bound for the accuracy of autoregressive modeling of discrete stationary vector random processes of the spectral matrix \(K(\theta)\) is given in terms of \(K(\theta)\). This permits an a priori estimation of the order of the autoregressive model. A simple relationship is derived that relates some Fourier coefficients of the target spectral matrix and its autoregressive counterpart. The results of the paper extend previously known results for the scalar orthogonal polynomials [see the author and \textit{P. D. Spanos}, Int. J. Non-Linear Mech. 26, No. 6, 911-930 (1991; Zbl 0825.65130)] to the matrix case.
discrete stationary vector random processes
scientific article; zbMATH DE number 903475