The intersection of past and future for multivariate stationary processes

TL;DR

This paper explores the intersection of past and future properties in multivariate stationary processes, extending spectral characterizations from univariate to multivariate cases to aid in deriving predictor coefficient matrices.

Contribution

It introduces spectral characterizations of the past-future intersection property for multivariate stationary processes, advancing theoretical understanding.

Findings

Extended spectral characterizations to multivariate processes

Provided new insights into predictor coefficient matrices

Enhanced theoretical framework for linear prediction

Abstract

We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral characterizations for this property from univariate processes to multivariate processes.