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On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix

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  • Preinerstorfer, David
  • Pötscher, Benedikt M.

Abstract

The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference, 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010, Econometric Theory, 26, 152–186) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from nontrivial flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in an even more general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests.

Suggested Citation

  • Preinerstorfer, David & Pötscher, Benedikt M., 2017. "On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix," Econometric Theory, Cambridge University Press, vol. 33(1), pages 1-68, February.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:01:p:1-68_00
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    Cited by:

    1. Pötscher, Benedikt M. & Preinerstorfer, David, 2018. "Controlling the size of autocorrelation robust tests," Journal of Econometrics, Elsevier, vol. 207(2), pages 406-431.
    2. Federico Martellosio, 2020. "Non-Identifiability in Network Autoregressions," Papers 2011.11084, arXiv.org, revised Jun 2022.
    3. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    4. David Preinerstorfer, 2018. "How to avoid the zero-power trap in testing for correlation," Papers 1812.10752, arXiv.org.
    5. Preinerstorfer, David, 2014. "Finite Sample Properties of Tests Based on Prewhitened Nonparametric Covariance Estimators," MPRA Paper 58333, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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