Power and Bias of Likelihood Based Inference in the Cointegration Model under Fractional Cointegration

This paper investigates how fractional cointegration affects the common maximum likelihood cointegration procedure. It is shown that the likelihood ratio test of no cointegration has considerable power against fractional alternatives. In contrast to the case of a cointegrated system, the usual maximum likelihood estimator gives severely biased estimates of the long-run relation under fractional cointegration. This suggests that the standard likelihood approach should be used with caution and that a test to separate fractionally cointegrated series from series that are cointegrated of an integer order should be executed prior to estimation.