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ON THE LACK OF POWER OF OMNIBUS SPECIFICATION TESTS

Published online by Cambridge University Press:  01 February 2009

J. Carlos Escanciano
J. Carlos Escanciano*
Affiliation:
Indiana University
*
*Address correspondence to Juan Carlos Escanciano, Department of Economics, Indiana University, 100 S. Woodlawn, Wylie Hall, Bloomington, IN 47405-7104, USA; e-mail: [email protected].
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Abstract

Designed to have power against all alternatives, omnibus consistent tests are the primary econometric tools for testing the correct specification of parametric conditional means when there is no information about the possible alternative. The main purpose of this paper is to show that, contrary to what is generally believed, omnibus specification tests only have substantial local power against alternatives in a finite-dimensional space (usually unknown to the researcher). We call such a space the principal space. We characterize and estimate the principal space for Cramér–von Mises tests. These results are some of the by-products of a detailed theoretical power analysis carried out in the paper. This investigation focuses on the class of the so-called integrated consistent tests under possibly heteroskedastic time series. A Monte Carlo experiment examines the finite-sample properties of tests and estimators of preferred alternatives. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates our findings.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 162 - 194
Copyright
Copyright © Cambridge University Press 2009

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