Vector Time Series and Model Representations

Abstract

We study models that describe relationships among a vector of k time series variables Y_1t, Y_2t, …, Y_kt of interest. Such multivariate processes arise when several related time series processes are observed simultaneously over time, instead of observing just a single series as is the case in univariate time series analysis. Multivariate time series processes are of considerable 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.