How useful are tests for unit‐root in distinguishing unit‐root processes from stationary but non‐linear processes?

Abstract

Standard unit‐root tests are known to be biased towards the non‐rejection of a unit‐root when they are applied to time series with non‐linear dynamics. Unfortunately, not much is known about the source of the power loss mainly because the analysis on nonstationarity and nonlinearity to this date has been fragmentary. By means of a Monte Carlo study, the current paper investigates the finite sample performance of five popular unit‐root tests against a wide class of non‐linear dynamic models. In contrast to the common perception, our simulation results suggest that what determines the power of unit‐root tests is not the specific type of nonlinearity in the alternative model, but how far the alternative model is away from the unit‐root process. The presence of nonlinearity seems immaterial to the performance of unit‐root tests if the non‐linear process is far away from the unit‐root process, which is in line with the fact established in linear framework. Among the five tests under study, the ADF test outperforms when the sample size is relatively small while the inf‐t due to Park and Shintani (2005) is more powerful for relatively large sample size regardless of the form of true models. We then illustrate the empirical relevance of our analysis by reexamining the issue of mean reversion in real interest rates, often referred to the Fisher hypothesis.

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