Rate of Mean Convergence of Finite Linear Predictors of Multivariate Stationary Stochastic Processes

摘要

This document considers a multivariate weakly stationary stochastic process (X sub n) with the spectral density matrix f satisfying the boundedness condition. It is shown that if the entries of f are analytic functions of theta on -pi,pi, then the rate of convergence of the one-step ahead linear least squares predictor of (X sub n) based on a finite segment of the past, and the partial sum of the infinite linear least squares predictor of the process to the Kolmogorov-Wiener predictor is at least exponential. (Author)