A matricial extension of the Helson-Szegö theorem and its application in multivariate prediction

Abstract

It is shown that the positivity of the angle between the past and future of a multivariate stationary process is sufficient for the existence of a mean-convergent autoregressive series representation of its linear predictor. A large class of multivariate processes whose past and future are at positive angle is characterized, thus providing a matricial extension of the Helson-Szegö theorem.