The Exact Maximum Likelihood-Based Test for Fractional Cointegration: Critical Values,Power and Size

The exact maximum likelihood (EML) procedure can be used as a residual-based test of the hypothesis of no cointegration against the alternative of fractional cointegration. Since the corresponding asymptotic properties have not yet been established, this paper provides simulated critical values, power and size relating to the EML-based test for fractional cointegration. Monte Carlo simulations indicate that the simulated density of the EML-based test is shifted to the left compared to the standard normal distribution and exhibits a strong excess of kurtosis in the absence of autoregressive components in the regression residuals. The power and size comparison indicates that the EML-based test is more powerful than other fractional cointegration tests (Lo, Lobato-Robinson and Geweke and Porter-Hudak) in small and medium sample sizes. Moreover, by simulating integrated time series with AR(1), and respectively MA(1), disturbances, it is shown that, whatever the sample size, the EML-based test exhibits the lowest size distortions for positive AR(1) and negative MA(1) coefficients, respectively.JEL classifications: C15; C22