Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior
Right-tailed unit root tests have proved promising for detecting exuberance in economic and ﬁnancial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model speciﬁcation used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under diﬀerent hypotheses and model speciﬁcations. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. Empirical applications to the Nasdaq and to Australian and New Zealand housing data illustrate these speciﬁcation issues and reveal their practical importance in testing.
Phillips, Peter C.B.; Shi, Shu-Ping; and Yu, Jun, "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior" (2012). Cowles Foundation Discussion Papers. 2201.