Using Difference‐Based Methods for Inference in Regression with Fractionally Integrated Processes

. This paper suggests a difference‐based method for inference in the regression model involving fractionally integrated processes. Under suitable regularity conditions, our method can effectively deal with the inference problems associated with the regression model consisting of nonstationary, stationary and intermediate memory regressors, simultaneously. Although the difference‐based method provides a very flexible modelling framework for empirical studies, the implementation of this method is extremely easy, because it completely avoids the difficult problems of choosing a kernel function, a bandwidth parameter, or an autoregressive lag length for the long‐run variance estimation. The asymptotic local power of our method is investigated with a sequence of local data‐generating processes (DGP) in what Davidson and MacKinnon [Canadian Journal of Economics. (1985) Vol. 18, pp. 38–57] call ‘regression direction’. The simulation results indicate that the size control of our method is excellent even when the sample size is only 100, and the pattern of power performance is highly consistent with the theoretical finding from the asymptotic local power analysis conducted in this paper.