Multiple Time Series Modeling With Reduced Ranks

Abstract

There has been growing interest in multiple time series modeling, particularly through use of vector autoregressive moving average models. The subject has found appeal and has applications in various disciplines, including engineering, physical sciences, business and economics, and the social sciences. In general, multiple time series analysis is concerned with modeling and estimation of dynamic relationships among m related time series y _1t, ... ,y _mt, based on observations on these series over T equally spaced time points t = 1,... ,T, and also between these series and potential input or exogenous time series variables x _1t,..., x _nt, observed over the same time period. In this chapter, we shall explore the use of certain reduced-rank modeling techniques for analysis of multiple time series in practice. We first introduce a general model for multiple time series modeling, but will specialize to multivariate autoregressive (AR) models for more detailed investigation.