Prediction theory of infinite variate weakly stationary stochastic processes

Abstract

In this paper we set down some of the main results of infinite variate weakly stationary stochastic processes. It is not assumed that the matrix spectral densities are necessarily bounded operator valued functions, but simply that they are infinite matrix-valued functions on the circle group with summable entries. Following an idea of R. Gangolli, we give analytic conditions for prediction error matrix to be non-singular.