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Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

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  • DUFOUR, Jean-Marie
  • FARHAT, Abdekjelik
  • HALLIN, Marc

Abstract

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2005-05.

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Length: 43 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mtl:montde:2005-05

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Keywords: autocorrelation ; serial dendence ; nonrametric test ; distribution-free test ; heterogeneity ; heteroskedasticity ; symmetric distribution ; robustness ; exact test ; bound ; exnential bound ; large deviations ; Chebyshev inequality ; Berry-Esséen ; interest rates.;

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References

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  1. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & HALLIN, Marc, 2005. "Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series," Cahiers de recherche 05-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
  3. Marc Hallin & Jean-Marie Dufour, 1992. "Simple exact bounds for distributions of linear signed rank statistics," ULB Institutional Repository 2013/2033, ULB -- Universite Libre de Bruxelles.
  4. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
  5. Dufour, J.M., 1988. "Non-Uniform Bounds for Nonparametric T Tests," Cahiers de recherche 8820, Universite de Montreal, Departement de sciences economiques.
  6. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-94, March.
  7. Dufour, J.M., 1979. "Rank Tests for Serial Dependence," Cahiers de recherche 7815, Universite de Montreal, Departement de sciences economiques.
  8. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
  9. Hallin, M. & Puri, M.L., 1992. "Rank Tests for Time Series Analysis , A Survey," Papers 9210, Universite Libre de Bruxelles - C.E.M.E..
  10. Dufour, J.M. & Hallin, M., 1992. "Improved Eaton Bounds for Linear Combinations of Bounded Random Variables with Statistical Applications," Cahiers de recherche 9224, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  11. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  12. Nathan Balke & Robert J. Gordon, 1986. "Appendix B Historical Data," NBER Chapters, in: The American Business Cycle: Continuity and Change, pages 781-850 National Bureau of Economic Research, Inc.
  13. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
  14. Dufour, J.M. & Roy, R., 1984. "Some Robust Exact Results on Sample Autocorrelations and Tests of Randomness," Cahiers de recherche 8412, Universite de Montreal, Departement de sciences economiques.
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Cited by:
  1. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & HALLIN, Marc, 2005. "Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series," Cahiers de recherche 05-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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