Optimal Residual Based Tests for Fractional Cointegration and Exchange Rate Dynamics

We propose a Lagrange Multiplier test of the null hypothesis of cointegration in fractionally cointegrated models. The test statistic utilizes fully modified residuals to cancel the endogeneity and serial correlation biases, and we show that standard asymptotic properties apply under the null and under local alternatives. With i.i.d. Gaussian errors the asymptotic Gaussian power envelope of all (unbiased) tests is achieved by the one-sided (two-sided) test. The finite sample properties are illustrated by a Monte Carlo study. In an application to the dynamics among exchange rates for seven major currencies against the US dollar, mixed evidence of the existence of a cointegrating relation is found