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ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS

Published online by Cambridge University Press:  26 February 2015

David Preinerstorfer  and
Benedikt M. Pötscher
David Preinerstorfer
Affiliation:
University of Vienna
Benedikt M. Pötscher*
Affiliation:
University of Vienna
*
*Address correspondence to Benedikt Pötscher, Department of Statistics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria; e-mail: benedikt.poetscher@univie.ac.at.
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Abstract

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Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 2 , April 2016 , pp. 261 - 358
Copyright
Copyright © Cambridge University Press 2015 

References

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