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

Recently, Shimotsu and Phillips (2005) 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 if the optimization covers an interval of width less than 9/2 and the mean of the process is known. With the intent to provide an efficient semiparametric estimator suitable for economic data, we extend the ELW estimator so that it accommodates an unknown mean and a polynomial time trend. We show that the resulting feasible ELW estimator is consistent and has a N(0,1/4) limit distribution for -1/2<d<2 (or -1/2<d<7/4 when the data has a polynomial trend) except for a few negligible intervals. We also develop a two-step feasible ELW estimator that avoids the exclusion of these intervals. A simulation study shows that the feasible ELW estimator inherits the desirable properties of the ELW estimator.