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POWER FUNCTIONS AND ENVELOPES FOR UNIT ROOT TESTS

Published online by Cambridge University Press:  31 January 2003

Ted Juhl  and
Zhijie Xiao
Ted Juhl
Affiliation:
University of Kansas
Zhijie Xiao
Affiliation:
University of Illinois at Urbana-Champaign
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Abstract

This paper studies power functions and envelopes for covariate augmented unit root tests. The power functions are calculated by integrating the characteristic function, allowing accurate evaluation of the power envelope and the power functions. Using the power functions, we study the selection among point optimal invariant unit root tests. An “optimal” point optimal test is proposed based on minimizing the integrated power difference. We find that when there are covariate effects, optimal tests use a local alternative where the power envelope has an approximate value of 0.75.We thank Pentti Saikkonen and two referees for helpful comments.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 2 , April 2003 , pp. 240 - 253
Copyright
© 2003 Cambridge University Press

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