Time Series Analysis: Forecasting and Control, Fourth Edition

CHAPTER FOURTEEN

Multivariate Time Series Analysis

Multivariate time series analysis is the study of statistical models and methods of analysis that describe the relationships among several time series. For many time series arising in practice, a more effective analysis may be obtained by considering individual series as components of a vector time series and analyzing the series jointly. We assume k time series variables, denoted as z_1t, z_2t, …, z_kt, are of interest, and we let Z_t = (z_1t, …, z_kt)′ denote the time series vector at time t, for t = 0,±1, …. Such multivariate processes arise when several related time series are observed simultaneously over time, instead of observing just a single series as is the case in univariate time series analysis studied in Parts One and Two of this book. Multivariate time series processes are of interest in a variety of fields such as engineering, the physical sciences, particularly the earth sciences (e.g., meteorology and geophysics), and economics and business. For example, in an engineering setting, one may be interested in the study of the simultaneous behavior over time of current and voltage, or of pressure, temperature, and volume, whereas in economics, we may be interested in the variations of interest rates, money supply, unemployment, and so on, or in sales volume, prices, and advertising expenditures for a particular commodity in a business context.

In the study of multivariate processes, a framework is needed for describing not ...