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

Author

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  • Kleiber, Christian
  • Krämer, Walter

Abstract

We consider the finite sample power of various tests against serial correlation in the disturbances of a linear regression when these disturbances follow a stationary long memory process. 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 for certain regressors. We also provide a means to detect this zero-power trap. Our results depend solely on the correlation structure and allow for fairly arbitrary nonlinearities.

Suggested Citation

  • Kleiber, Christian & Krämer, Walter, 2004. "Finite sample of the Durbin-Watson test against fractionally integrated disturbances," Technical Reports 2004,15, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  • Handle: RePEc:zbw:sfb475:200415
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    References listed on IDEAS

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    1. Kleiber, Christian, 2001. "Finite sample efficiency of OLS in linear regression models with long-memory disturbances," Economics Letters, Elsevier, vol. 72(2), pages 131-136, August.
    2. King, Maxwell L. & Evans, Merran A., 1988. "Locally Optimal Properties of the Durbin-Watson Test," Econometric Theory, Cambridge University Press, vol. 4(03), pages 509-516, December.
    3. Hisamatsu, Hiroyuki & Maekawa, Koichi, 1994. "The distribution of the Durbin-Watson statistic in integrated and near-integrated models," Journal of Econometrics, Elsevier, vol. 61(2), pages 367-382, April.
    4. 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.
    5. King, Maxwell L., 1985. "A point optimal test for autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 27(1), pages 21-37, January.
    6. W. Tsay, 1998. "On the power of durbin-watson statistic against fractionally integrated processes," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 361-386.
    7. Kramer, Walter & Zeisel, Helmut, 1990. "Finite sample power of linear regression autocorrelation tests," Journal of Econometrics, Elsevier, vol. 43(3), pages 363-372, March.
    8. Bartels, Robert, 1992. "On the power function of the Durbin-Watson test," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 101-112.
    9. King, M. L., 1981. "The alternative Durbin-Watson test : An assessment of Durbin and Watson's choice of test statistic," Journal of Econometrics, Elsevier, vol. 17(1), pages 51-66, September.
    10. Nakamura, Shisei & Taniguchi, Masanobu, 1999. "Asymptotic Theory For The Durbin Watson Statistic Under Long-Memory Dependence," Econometric Theory, Cambridge University Press, vol. 15(06), pages 847-866, December.
    11. Nabeya, Seiji & Tanaka, Katsuto, 1990. "Limiting power of unit-root tests in time-series regression," Journal of Econometrics, Elsevier, vol. 46(3), pages 247-271, December.
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    Cited by:

    1. 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.

    More about this item

    Keywords

    Durbin-Watson test; power; autocorrelation; long memory;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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