A unified framework for testing in the linear regression model under unknown order of fractional integration

We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional integration. We propose a Lagrange Multiplier-type test whose limiting distribution is independent of the order of integration of the errors. Different testing scenarios for the case of deterministic and stochastic regressors are considered. Simulations demonstrate that the proposed test works well for a variety of different cases, thereby emphasizing its generality.