Abstract

This paper exploits the fact that any time series with a unit root can de decomposed into a stationary series and a random walk. Since the random walk component can have arbitrarily small variance, tests for unit roots or trend stationarity have arbitrarily low power in finite samples. Furthermore, there are unit root processes whose likelihood functions and autocorrelation functions are arbitrarily close to those of any given stationary processes and vice versa, so there are stationary and unit root processes for which the result of any inference is arbitrarily close in finite samples.

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^* I thank John Huizinga and Jim Stock for detailed and valuable comments, and Robert Townsend for the discussion that provoked this paper.This research was partially supported by National Science Foundation grant SES-8809912.