One Channel At-A-Time Multichannel Autoregressive Modeling of Stationary and Nonstationary Time Series

Abstract

This paper exploits a known but insufficiently attended to idea for the autogressive modeling of multivariate stationary and nonstationary covariance time series. (The term multichannel is common in the engineering literature. Here, we use both terminologies, multivariate and muItich annel.) The idea is to model multichannel thing s one channel ar-a-time as an instantaneous response-orthogonal innovations autoregressive model. Such modeling can be realized using only scalar computations. That idea was implicit in Pagano (1978) and was explicit in a program MULMAR by Kitagawa (Akaike et al, 1979 ), in Newton (1982) and also Sakai (1982). Each of those papers only treated multichannel stationary time series AR modeling. Here , we exploit that idea to address time series analysis problems via the realization of autoregressive models of botti multi channel stationary and multi channel nonstationary covariance times series data.