Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behaviour


  • We thank two anonymous referees and the editor for helpful suggestions. We are grateful to Heather Anderson, Farshid Vahid, Hashem Pesaran, and Tom Smith for helpful discussions. Phillips acknowledges support from the NSF under Grant No. SES 09-56687. Shi acknowledges the Financial Integrity Research Network (FIRN) for funding support. Yu thanks the Singapore Ministry of Education for Academic Research Fund under grant number MOE2011-T2-2-096.

JEL Classification numbers: C15, C22.


This article aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focusing on the recursive right-tailed ADF test of Phillips et al. (2011b). We analyze and compare the limit theory of the recursive test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined and some recommendations for empirical practice are given. Some new results on the consistent estimation of localizing drift exponents are obtained, which are useful in assessing model specification. Empirical applications to stock markets illustrate these specification issues and reveal their practical importance in testing.