Estimation of long memory in the presence of a smooth nonparametric trend

Abstract

We consider semi parametric estimation of the long-memory parameter of a stationary process in the presence of an additive nonparametric mean function. We use a semi parametric Whittle type estimator, applied to the tapered, differenced series. Since the mean function is not necessarily a polynomial of finite order, no amount of differencing will completely remove the mean. We establish a central limit theorem for the estimator of the memory parameter, assuming that a slowly increasing number of low frequencies are trimmed from the estimator's objective function. We find in simulations that tapering and trimming are essential for the good performance of the estimator in practice.