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On Size and Power of Heteroscedasticity and Autocorrelation Robust Tests

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  • Preinerstorfer, David
  • Pötscher, Benedikt M.

Abstract

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroscedasticity 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 heteroscedastic disturbances.

Suggested Citation

  • Preinerstorfer, David & Pötscher, Benedikt M., 2013. "On Size and Power of Heteroscedasticity and Autocorrelation Robust Tests," MPRA Paper 45675, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:45675
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    References listed on IDEAS

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    Cited by:

    1. repec:eee:econom:v:198:y:2017:i:2:p:277-295 is not listed on IDEAS
    2. Pötscher, Benedikt M. & Preinerstorfer, David, 2016. "Controlling the Size of Autocorrelation Robust Tests," MPRA Paper 75657, University Library of Munich, Germany.
    3. Pötscher, Benedikt M. & Preinerstorfer, David, 2017. "Further Results on Size and Power of Heteroskedasticity and Autocorrelation Robust Tests, with an Application to Trend Testing," MPRA Paper 81053, University Library of Munich, Germany.
    4. Hwang, Jungbin & Sun, Yixiao, 2017. "Asymptotic F and t tests in an efficient GMM setting," Journal of Econometrics, Elsevier, vol. 198(2), pages 277-295.

    More about this item

    Keywords

    Size distortion; power deficiency; invariance; robustness; autocorrelation; heteroscedasticity; HAC; fixed-bandwidth; long-run-variance; feasible GLS;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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