The motivation for multivariate forecasting is that there is information in multiple economic time series that can be used to improve forecasts of the variable or variables of interest. Economic theory, formal and informal, suggests a large number of such relations. Multivariate forecasting methods in econometrics are usefully divided into four broad categories: structural econometric models; small linear time series models; small nonlinear time series models; and forecasts based on leading economic indicators.
Structural econometric models attempt to exploit parametric relationships suggested by economic theory to provide a priori restrictions. These models can be hundred-plus equation simultaneous systems, or very simple relations such as an empirical Phillips curve relating changes of inflation to the unemployment rate and supply shocks. Because simultaneous equations are the topic of Chapter 6 by Mariano in this volume, forecasts from simultaneous equations systems will be discussed no further here. Neither will we discuss further nonlinear multivariate models; although the intuitive motivation for these is sound, these typically have many parameters to be estimated and as such often exhibit poor out-of-sample performance (for a study of multivariate NNs, see Swanson and White (1995, 1997); for some positive results, see Montgomery et al., 1998). This chapter therefore briefly reviews multivariate forecasting with small linear time series models, in particular, using VARs, and forecasting with leading indicators. For additional background on VARs, see the chapter in this volume by Lutkepohl.