SpeciÖcation Sensitivities in Right-Tailed Unit Root Testing for Financial Bubbles

Right-tailed unit root tests have proved promising for detecting exuberance in economic and Önancial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model speciÖcation 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 di§erent hypotheses and model speciÖcations. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. An empirical application to Nasdaq data reveals the practical importance of model speciÖcation on test outcomes.