A Monte Carlo study on the selection of cointegrating rank using information criteria

We conduct Monte Carlo simulations to evaluate the use of information criteria (Akaike information criterion [AIC] and Schwarz information criterion [SC]) as an alternative to various probability-based tests for determining cointegrating rank in multivariate analysis. First, information criteria are used to determine cointegrating rank given the lag order in a levels vector autoregression. Second, information criteria are used to determine the lag order and cointegrating rank simultaneously. Results show that AIC has an advantage over trace tests for cointegrated or stationary processes in small samples. AIC does not perform well in large samples. The performance of SC is close to that of the trace test. SC shows better large sample results than AIC and the trace test, even if the series are close to nonstationary series or they contain large negative moving average components. We also find evidence that supports the joint estimation of lag order and cointegrating rank by the SC criterion. We conclude that information criteria can complement traditional parametric tests.