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

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  • DUFOUR, Jean-Marie
  • FARHAT, Abdeljelil
  • 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 Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 05-2005.

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Length: 46 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mtl:montec:05-2005

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Keywords: autocorrelation; serial dependence; nonparametric test; distribution-free test; heterogeneity; heteroskedasticity; symmetric distribution; robustness; exact test; bound; exponential bound; large deviations; Chebyshev inequality; Berry-Esséen; interest rates;

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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. Dufour, J.M., 1979. "Rank Tests for Serial Dependence," Cahiers de recherche 7815, Universite de Montreal, Departement de sciences economiques.
  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. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Dufour, J-M., 1988. "Non-Uniform Bounds For Nonparametric T Tests," Cahiers de recherche 8820, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Dufour, Jean-Marie & Roy, Roch, 1985. "Some robust exact results on sample autocorrelations and tests of randomness," Journal of Econometrics, Elsevier, vol. 29(3), pages 257-273, September.
  10. Marc Hallin & Jean-Marie Dufour, 1993. "Improved Eaton bounds for linear combinations of bounded random variables, with statistical applications," ULB Institutional Repository 2013/2043, ULB -- Universite Libre de Bruxelles.
  11. Campbell, B. & Dufour, J.M., 1994. "Excat Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," Cahiers de recherche 9407, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  12. 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.
  13. Hallin, M. & Puri, M.L., 1992. "Rank Tests for Time Series Analysis , A Survey," Papers 9210, Universite Libre de Bruxelles - C.E.M.E..
  14. 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.
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Cited by:
  1. Jean-Marie Dufour & Abdeljelil Farhat & Marc Hallin, 2005. "Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series," CIRANO Working Papers 2005s-04, CIRANO.

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