COWLES FOUNDATION FOR RESEARCH IN
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COWLES FOUNDATION DISCUSSION PAPER NO. 1842 Specification Sensitivity in Right-Tailed Unit Root Testing Peter C.B. Phillips, Shu-Ping Shi, and Jun Yu January 2012 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. |
