Generalized Schur Parametrization of Nonstationary Second-Order Processes

Abstract

Given a stationary stochastic process, a classical algorithm of I. Schur can be used to set up a reversible mapping between its covariance values {r₀= 1,r₁,...,r_T} and a set of Schur parameters {k₁,...,k_T}, |k_i|≤1. The Schur parameters have been very useful in the efficient modeling and prediction of stationary processes in the so-called lattice (or ladder) forms. In this paper we show how the concept of displacement rank introduced in earlier work (Bull. AMS, Sept. 1979) can be used to obtain a natural generalization of the Schur parametrization for nonstationary processes. This leads to useful generalized lattice form models for such processes.

This work was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command under Contract AF49-620-79-C-0058, and in part by the U.S. Army Research Office, under Contract DAAG29-79-C-0215.