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Locally Optimal Properties of the Durbin-Watson Test

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  • King, Maxwell L.
  • Evans, Merran A.

Abstract

Although originally designed to detect AR(1) disturbances in the linear-regression model, the Durbin-Watson test is known to have good power against other forms of disturbance behavior. In this paper, we identify disturbance processes involving any number of parameters against which the Durbin–Watson test is approximately locally best invariant uniformly in a range of directions from the null hypothesis. Examples include the sum of q independent ARMA(1,1) processes, certain spatial autocorrelation processes involving up to four parameters, and a stochastic cycle model.

Suggested Citation

  • 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.
  • Handle: RePEc:cup:etheor:v:4:y:1988:i:03:p:509-516_01
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    References listed on IDEAS

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    1. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
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    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    4. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    7. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
    8. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-1056, September.
    9. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    10. Peter C.B. Phillips & Joon Y. Park, 1986. "Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors," Cowles Foundation Discussion Papers 802, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Banerjee, Anurag N. & Magnus, Jan R., 1999. "The sensitivity of OLS when the variance matrix is (partially) unknown," Journal of Econometrics, Elsevier, vol. 92(2), pages 295-323, October.
    2. Banerjee, A.N. & Magnus, J.R., 1996. "Testing the Sensitivity of OLS when the Variance Maxtrix is (Partially) Unknown," Discussion Paper 1996-54, Tilburg University, Center for Economic Research.
    3. 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.
    4. Phillips, Peter C. B. & Loretan, Mico, 1991. "The Durbin-Watson ratio under infinite-variance errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 85-114, January.
    5. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.
    6. 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.

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