Inference on Non-Stationary Time Series with Moving Mean

Abstract

A semiparametric model is proposed in which a parametric …ltering of a nonstationary time series, incorporating fractionally di¤erencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I(1) and other hypotheses are thereby justi…ed. Estimation of the trend function is also considered. We include a Monte Carlo study of …nite-sample performance.