Testing for a Unit Root in Time Series Regression

TLDR

The paper proposes new tests for detecting the presence of a unit root in general time‑series models. The authors develop nonparametric unit‑root tests that work for weakly dependent, heterogeneously distributed data, accommodate drift and trend, and derive limiting distributions under the null and local alternatives, with finite‑sample performance evaluated by simulation. The tests achieve local asymptotic power comparable to Dickey–Fuller procedures, as shown by the derived noncentral distribution theory.

Abstract

This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.