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Finite-sample power of the Durbin--Watson test against fractionally integrated disturbances

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  • Christian Kleiber
  • Walter Krämer

Abstract

We consider the finite-sample power of various tests against serial correlation in the disturbances of a linear regression model when these disturbances follow certain stationary long-memory processes. It emerges that the power depends on the form of the regressor matrix and that, for the Durbin--Watson test and many other tests that can be written as ratios of quadratic forms in the disturbances, the power can drop to zero as the long-memory parameter approaches the boundary of the stationarity region. The problem does not arise when the regression includes an intercept. We also provide a means to detect this zero-power trap for given regressors. Our analytical results are illustrated using fractionally integrated white noise and ARFIMA(1, d, 0) disturbances with artificial regressors and with a real data set. Copyright 2005 Royal Economic Society

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  • 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.
    • Handle: RePEc:ect:emjrnl:v:8:y:2005:i:3:p:406-417
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    Cited by:

    1. 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.
    2. Anurag Banerjee, 2004. "Sensitivity of OLS estimates against ARFIMA error process as small sample Test for long memory," Econometric Society 2004 Australasian Meetings 159, Econometric Society.
    3. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
    4. David Preinerstorfer, 2018. "How to avoid the zero-power trap in testing for correlation," Papers 1812.10752, arXiv.org.
    5. Cappuccio, Nunzio & Lubian, Diego & Mistrorigo, Mirko, 2015. "The power of unit root tests under local-to-finite variance errors," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 205-217.

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