Statistical Analysis of Cointegrated VAR Processes with Markovian Regime Shifts

This paper suggests a new methodological approach to the analysis of cointegrated linear systems subject to changes in regime. We consider cointegrated vector autoregressive processes where Markovian shifts occur in the equilibrium mean and the drift of the system. A two-stage maximum likelihood estimation technique is proposed. In the first stage, based on a finite order VAR approximation of the cointegrated VARMA representation, the Johansen cointegration analysis is invoked to determine the cointegration rank and to estimate the cointegration matrix. An EM algorithm delivers the maximum likelihood estimates of the remaining parameters. The methodology is illustrated with an investigation of international and global business cycles.