Inference on Non-Stationary Time Series with Moving Mean

Abstract

A semi-parametric model is proposed in which a parametric filtering of a non-stationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a non-parametric 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. Unit root tests with standard asymptotic distributions are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of …nite-sample performance.

Keywords: fractional time series, fi…xed design non-parametric regression, non-stationary time series, unit root tests

JEL Classification: C14, C22