Over-rejections by the weighted symmetric unit root test in multiple structural breaks

Abstract

This study investigates the behaviour of the weighted symmetric unit root test (Pantula et al., 1994) when the data generating process has a unit root and multiple structural breaks in the level of its trend function. The results obtained from this study reveal that the test can be biased towards over-rejections of the unit root null hypothesis in large samples as well as small samples.

Acknowledgements

This article owes much to helpful comments of Mitsuru Nakagawa (Osaka City University) on my presentation at the 2004 Fall Meeting of the Japanese Economic Association (Okayama). The research for the article was supported in part by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Grant-in-Aid for Encouragement of Young Scientists #14730032 (Japan).

Notes

¹ Some testing methods are available for testing a unit root when the existence of multiple structural breaks in a sample period is suspected. For example, Lumsdaine and Papell's (1997) method can test the nonstationarity of the time series that has two structural breaks at unknown dates under the alternative model. Lee and Strazicich's (2003) minimum Lagrange Multiplier (LM) unit root test can be applied to the series with two endogenous breaks under both the null and alternative hypotheses.

² We have also analysed three other cases: the case in which , where for , and 0 otherwise (multiple slope changes); the case in which and the case in which , where the summation Σ is from h = 1 to H. Consequently, it has been found that the WS tests are asymptotically invariant to the existence of these three types of multiple breaks.

³ The DF -type statistic can also be defined by replacing with . Since the behaviour of this statistic is rather similar to that of the t _WS-statistic, it is not reported here.

⁴ In the case of more than two breaks, the corresponding deterministic terms, which may become the cause of the misjudgment on the hypothesis test, are present in the limiting distribution.