Matrix polynomials orthogonal on the unit circle and accuracy of autoregressive models

Some new results in the theory of matrix polynomials orthogonal on the unit circle are derived to provide a basis for assessing the accuracy of autoregressive models. In particular, a bound to the weighted norm of the difference between matrix polynomials and their infinite degree limit is obtained which can be used to estimate a priori their rate of convergence. Finally, the connections between some Fourier coefficients of the weight matrix and of its autoregressive approximation are investigated.