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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) (for the Durbin-Watson test) and Krämer (2005) (for the Cliff-Ord test) have shown that the power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010) 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 serious flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in a fairly 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.

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  • Preinerstorfer, David & Pötscher, Benedikt M., 2014. "On the Power of Invariant Tests for Hypotheses on a Covariance Matrix," MPRA Paper 55059, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:55059
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    References listed on IDEAS

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    1. Federico Martellosio, 2012. "Testing for Spatial Autocorrelation: The Regressors that Make the Power Disappear," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 215-240.
    2. Kramer, W., 1985. "The power of the Durbin-Watson test for regressions without an intercept," Journal of Econometrics, Elsevier, vol. 28(3), pages 363-370, June.
    3. Mynbaev, Kairat, 2011. "Distributions escaping to infinity and the limiting power of the Cliff-Ord test for autocorrelation," MPRA Paper 44402, University Library of Munich, Germany, revised 18 Sep 2012.
    4. Kramer, Walter & Zeisel, Helmut, 1990. "Finite sample power of linear regression autocorrelation tests," Journal of Econometrics, Elsevier, vol. 43(3), pages 363-372, March.
    5. Bartels, Robert, 1992. "On the power function of the Durbin-Watson test," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 101-112.
    6. Martellosio, Federico, 2011. "Efficiency of the OLS estimator in the vicinity of a spatial unit root," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1285-1291, August.
    7. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 32(2), pages 261-358, April.
    8. Kadiyala, Koteswara Rao, 1970. "Testing for the Independence of Regression Disturbances," Econometrica, Econometric Society, vol. 38(1), pages 97-117, January.
    9. Martellosio, Federico, 2010. "Power Properties Of Invariant Tests For Spatial Autocorrelation In Linear Regression," Econometric Theory, Cambridge University Press, vol. 26(1), pages 152-186, February.
    10. King, Maxwell L., 1985. "A point optimal test for autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 27(1), pages 21-37, January.
    11. Martellosio, Federico, 2011. "Nontestability Of Equal Weights Spatial Dependence," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1369-1375, December.
    12. Christian Kleiber & Walter Krämer, 2005. "Finite-sample power of the Durbin--Watson test against fractionally integrated disturbances," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 406-417, December.
    13. Tillman, John A, 1975. "The Power of the Durbin-Watson Test," Econometrica, Econometric Society, vol. 43(5-6), pages 959-974, Sept.-Nov.
    14. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
    15. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. David Preinerstorfer, 2018. "How to avoid the zero-power trap in testing for correlation," Papers 1812.10752, arXiv.org.
    2. Pötscher, Benedikt M. & Preinerstorfer, David, 2018. "Controlling the size of autocorrelation robust tests," Journal of Econometrics, Elsevier, vol. 207(2), pages 406-431.
    3. Federico Martellosio, 2020. "Non-Identifiability in Network Autoregressions," Papers 2011.11084, arXiv.org, revised Jun 2022.
    4. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, 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.

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    More about this item

    Keywords

    power function; invariant test; autocorrelation; spatial correlation; zero-power trap; indistinguishability; Durbin-Watson test; Cliff-Ord test;
    All these keywords.

    JEL classification:

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

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