VARS, cointegration, and common cycle restrictions

This article argues that the vector autoregressive (VAR) models with cointegration and common cycles (or weaker forms of rank restrictions) can be usefully viewed as observable factor models. The factors are linear combinations of lagged levels and lagged differences, and as such, these observable factors have forecasting potential. This potential is illustrated in both a Monte Carlo and empirical setting, and the difficulties in developing "rules of thumb" for forecasting in multivariate systems are demonstrated. The article is organized as follows. Section 2 provides a synopsis of the literature on VARs with common trends, common cycles, and other common features. Section 3 extends the Monte Carlo analysis in Lin and Tsay (1996) to illustrate how model selection and the imposition of short-and long-run restrictions affect forecasts. Section 4 studies the forecasting performance of several reduced-rank multivariate models of an updated version of the Litterman (1986) data set, while Section 5 concludes.