Testing for a Unit Root in a Time Series With a Changing Mean

Abstract

This study considers testing for a unit root in a time series characterized by a structural change in its mean level. My approach follows the “intervention analysis” of Box and Tiao (1975) in the sense that I consider the change as being exogenous and as occurring at a known date. Standard unit-root tests are shown to be biased toward nonrejection of the hypothesis of a unit root when the full sample is used. Since tests using split sample regressions usually have low power, I design test statistics that allow the presence of a change in the mean of the series under both the null and alternative hypotheses. The limiting distribution of the statistics is derived and tabulated under the null hypothesis of a unit root. My analysis is illustrated by considering the behavior of various univariate time series for which the unit-root hypothesis has been advanced in the literature. This study complements that of Perron (1989), which considered time series with trends.