Testing for a Unit Root in Time Series Regression

This Paper Proposes Some New Tests for Detecting the Presence of a Unit Root in Quite General Time Series Modesl. 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 Accomodate 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. Th Latter Noncentral Distribution Theory Yields Local Asymptotic Power Functions for the Tests. These Are Compared with Alternative Procedures Due to Dickey and Fuller. an Exemple Is Provided.