CHAPTER 3ANALYSIS OF MULTIVARIATE TIME SERIES

In this chapter, we consider jointly multiple time series with the goal of finding the linear dynamic relationships between them and exploring ways to improve the accuracy in forecasting. Our focus is on low-dimensional time series. The extension to high-dimensional case will be discussed later. See Chapters 6 and 7. In the literature, the analysis of multiple time series is also called the multivariate time series analysis and has been extensively studied. See, for instance, Hannan and Deistler (1988), Tiao and Box (1981), Reinsel (1993), Lütkepohl (2005), Tsay (2014), and the references therein. Our discussion here is brief and emphasizes on applications.

Let = be a -dimensional time series. A general class of linear models for is the vector autoregressive moving-average (VARMA) model