A New Approach to Unit Root Tests in Univariate Time Series Robust to Structural Changes

Abstract

Using methodology in panel unit root tests we propose a new approach to univariate unit root tests. Our method leads to an asymptotically normal distribution of the least squares estimator and is robust to contaminated data having structural changes or outliers while the power of the test does not drastically worsen. The main idea is that under the assumption that the process has a unit root we transform an AR(1) process [y t: 1 &#60;= t &#60;= T] to a double-index process [y [ij]: 1&#60;= i &#60;= m, 1 &#60;= j <= n, mn=T] in such a way that the segments are independent for $i=1,2, ..., m. For this transformed data, we apply the same sequential limit as in Levin and Lin (1992, 2002). First, as n goes to infinity we obtain asymptotic results for each i. These have the same form as in conventional univariate unit root tests. Second, as m goes to infinity, we obtain an asymptotically normal distribution for the OLS estimator by the Lindeberg-Feller CLT. An advantage of this technique is that an undetected break has a relatively minor effect which, in fact, disappears as m increases. We also show that for a general ARMA (p,q) model we still obtain the asymptotic normality of the unit root statistics under the sequential limit assumption.