A Monte Carlo Study of the Effects of Structural Breaks on Tests for Unit Roots

Abstract

The effects of a shift in the intercept of an autoregressive process on the rejection frequencies of standard tests for unit roots are investigated using Monte Carlo methods. Such tests lose power compared with the equivalent parameter values when no breaks occur. F-tests for structural breaks fail to detect shifts that are large enough to mimic unit roots. The response surface summarizing a conventional Monte Carlo highlights the effects on Dickey-Fuller (DF) and Augmented Dickey-Fuller (ADF) tests of the magnitudes of the autoregressive parameter, the break, the cumulative break, the estimation sample, and the percentage of the sample contaminated by the break. Diagnostic tests on the response surface support its specification. A recursive Monte Carlo computes sequences of rejection frequencies of DF and Chow tests and shows that these are low. Thus, care is required in interpreting unit-root tests since failure to reject does not entail that the null is true.