ABSTRACT
InChapters 1 through 9,wehave considered time series ‘‘one at a time.’’ In some situations, it is important to understand andmodel not only the autocorrelation structure down the time axis but also the relationships among a collection of time series along the same time axis. For example, in Figure 10.1a-c, we show monthly data from January 1, 1991 throughApril 1, 2010, on interest rates in the United States for 6-month CDs, Moody’s seasoned Aaa corporate bonds, and 30-year conventional mortgages, respectively. The understanding of such data may be improved by considering not only the autocorrelation structure of the univariate interest rate series but also the interrelationships among the three as they respond to market and economic conditions across time. In this chapter, we extend the definitions and techniques presented earlier in
the univariate setting to multivariate time series. Among the topics covered in this chapter are basic terminology and stationarity conditions for multivariate time series, multivariate autoregressive-moving average models (focusing on autoregressive models), and their applications. We also discuss the problem of assessingwhether two time series are correlated alongwith state-spacemodels.
Loosely speaking, a multivariate time series can be thought of as a collection of vector-valued observations made sequentially in time. To be more formal, we give the following definition that extendsDefinition 1.1 to themultivariate case.
Definition 10.1 Amultivariate stochastic process {Xt; t 2 T} is a collection of vector-valued random variables
