The robustness of modified unit root tests in the presence of GARCH

Abstract

The research of Kim and Schmidt (J. Economet., 1993, 59, 287–300) is extended to examine the properties of modified Dickey–Fuller unit root tests in the presence of generalized autoregressive conditional heteroskedasticity (GARCH). Using Monte Carlo simulation, the properties of the tests are examined for a range of GARCH processes over alternative sample sizes. Oversizing is observed for all tests, with the extent of size distortion driven by the volatility, rather than the persistence, of the underlying GARCH process. While the original Dickey–Fuller test is found to exhibit greater size distortion than the modified tests, the modified tests are found to be substantially oversized when the GARCH process exhibits a high degree of volatility, even for large samples.

Keywords:

• GARCH
• Unit root tests
• Size distortion

Acknowledgement

I am grateful to two anonymous referees for suggestions which have lead to improvements in the content and presentation of the present paper.