Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend

Recently Shimotsu and Phillips (2002, Essex Discussion Paper 535) developed a new semiparametric estimator, the exact local Whittle (ELW) estimator, of the memory parameter (d) in fractionally integrated processes. The ELW estimator has been shown to be consistent and have the same N(0, 1/4 ) limit distribution for all values of d. With economic applications in mind, we extend the ELW estimator so that it accommodates an unknown mean and a linear time trend. We show the resulting feasible ELW estimator is consistent for d > -1/2 and has a N(0, 1/4 ) limit distribution for d in (-1/2, 2) (d in (-1/2, 7/4) when the data have a linear trend) except for a few negligible intervals. A simulation study shows that the feasible ELW estimator inherits the desirable properties of the ELW estimator also in small samples.