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The Durbin-Watson ratio under infinite-variance errors

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  • Phillips, Peter C. B.
  • Loretan, Mico

Abstract

This paper studies the properties of the von Neumann ratio for time series with infinite variance. The asymptotic theory is developed using recent results on the weak convergence of partial sums of time series with infinite variance to stable processes and of sample serial correlations to functions of stable variables. Our asymptotics cover the null of iid variates and general moving average (MA) alternatives. Regression residuals are also considered. In the static regression model the Durbin-Watson statistic has the same limit distribution as the von Neumann ratio under general conditions. However, the dynamic models, the results are more complex and more interesting. When the regressors have thicker tail probabilities than the errors we find that the Durbin-Watson and von Neumann ration asymptotics are the same.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 47 (1991)
Issue (Month): 1 (January)
Pages: 85-114

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Handle: RePEc:eee:econom:v:47:y:1991:i:1:p:85-114

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. King, Maxwell L. & Wu, Ping X., 1991. "Small-disturbance asymptotics and the Durbin-Watson and related tests in the dynamic regression model," Journal of Econometrics, Elsevier, vol. 47(1), pages 145-152, January.
  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. Bartels, Robert & Goodhew, John, 1981. "The Robustness of the Durbin-Watson Test," The Review of Economics and Statistics, MIT Press, vol. 63(1), pages 136-39, February.
  4. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
  5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  6. Donald W.K. Andrews, 1986. "On the Performance of Least Squares in Linear Regression with Undefined Error Means," Cowles Foundation Discussion Papers 798, Cowles Foundation for Research in Economics, Yale University.
  7. Kariya, Takeaki, 1988. "The Class of Models for which the Durbin-Watson Test is Locally Optimal," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 167-75, February.
  8. Peter C.B. Phillips & Vassilis A. Hajivassiliou, 1987. "Bimodal t-Ratios," Cowles Foundation Discussion Papers 842, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
  2. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.
  3. Jonathan B. Hill, 2005. "On Tail Index Estimation Using Dependent,Heterogenous Data," Working Papers 0512, Florida International University, Department of Economics.
  4. Mikael Linden, 1992. "Stochastic and deterministic trends in Finnish macroeconomic time series," Finnish Economic Papers, Finnish Economic Association, vol. 5(2), pages 110-116, Autumn.
  5. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  6. Jonathan B. Hill, 2005. "Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Strochastic Processes with an Application," Working Papers 0513, Florida International University, Department of Economics.
  7. Huston McCulloch, J. & Panton, Don B., 1997. "Precise tabulation of the maximally-skewed stable distributions and densities," Computational Statistics & Data Analysis, Elsevier, vol. 23(3), pages 307-320, January.

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