Residual-based tests for fractional cointegration

This paper reports an extensive Monte Carlo study of six residual-based tests of the hypothesis of no cointegration against the alternative of fractional cointegration. Critical values, power and size are simulated and compared. It turns out that the Lobato–Robinson LM test, the Geweke–Porter-Hudak test and the two Phillips–Perron tests exhibit severe size distortions. On the other hand, the augmented Dickey–Fuller test and the modified rescaled range test show only moderate size distortions but are generally less powerful. In addition, the impact and possible treatment of trends in the individual series, and in the cointegration equilibrium, are discussed.