A Note on the Asymptotic Distributions of Unit Root Tests in the Additive Outlier Model With Breaks

Abstract

This note discusses tests for a unit root allowing the possibility of a onetime change in the intercept and/or the slope of the trend function in the additive outlier model considered in Perron (1989). We discuss and correct an error in the stated asymptotic distributions of the tests in this case. We propose a simple modification of the procedure which yields statistics having the same asymptotic distributions as stated in Perron (1989). We also discuss the adequacy of the asymptotic approximations and various extensions to the case where the breakpoint is unknown with corresponding asymptotic critical values.