Multiple cointegrating vectors, error correction, and forecasting with Litterman's model

Abstract

Johansen's (1988, Journal of Economic Dynamics and Control 12, 231–254) multivariate test for cointegration is applied to the six variables in Litterman's (1980, Working Paper, Massachusetts Institute of Technology) original Bayesian vector autoregression (BVAR) model. Two cointegrating vectors are obtained and used to specify error correction mechanism (ECM) and Bayesian ECM (BECM) models. The forecasting performance of these models is compared to vector autoregression (VAR) in levels, BVAR in levels, BVAR in differences and an “unrestricted” BECM model having the maximum n − 1 error correction terms. The BECM model outperforms all other specifications over both short- and long-term horizons. The superior performance of the BECM model over the unrestricted BECM model suggests that the inappropriate inclusion of error correction terms substantially reduces long-term forecasting accuracy. The forecasting performance of the ECM and BECM models relative to VAR and BVAR in levels suggests that error correction is the best approach for modeling both short- and long-run dynamics in multivariate cointegrated systems. Finally, evidence is presented supporting Engle and Yoo's (1987, Journal of Econometrics 35, 143–159) expectation that the ECM specification outperforms Litterman's BVAR.