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Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series

  • Marc Hallin
  • Abdeljelil Farhat
  • Jean-Marie Dufour

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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Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/2143.

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Date of creation: 2006
Date of revision:
Publication status: Published in: Journal of Econometrics (2006) v.130,p.123-142
Handle: RePEc:ulb:ulbeco:2013/2143
Contact details of provider: Postal: CP135, 50, avenue F.D. Roosevelt, 1050 Bruxelles
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  1. DUFOUR, Jean-Marie & FARHAT, Abdekjelik & HALLIN, Marc, 2005. "Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series," Cahiers de recherche 2005-05, Universite de Montreal, Departement de sciences economiques.
  2. Dufour, J.M., 1988. "Non-Uniform Bounds for Nonparametric T Tests," Cahiers de recherche 8820, Universite de Montreal, Departement de sciences economiques.
  3. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 2003-12, Universite de Montreal, Departement de sciences economiques.
  4. 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.
  5. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Universite de Montreal, Departement de sciences economiques.
  6. Dufour, J.M. & Hallin, M., 1990. "Simple Exact Bounds for Distributions of Linear Signed Rank Statistics," Cahiers de recherche 9003, Universite de Montreal, Departement de sciences economiques.
  7. 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.
  8. 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.
  9. Dufour, J.M. & Hallin, M., 1992. "Improved Eaton Bounds for Linear Combinations of Bounded Random Variables with Statistical Applications," Cahiers de recherche 9224, Universite de Montreal, Departement de sciences economiques.
  10. Dufour, J.-M., 1986. "Exact tests and confidence sets in linear regressions with autocorrelated errors," CORE Discussion Papers 1986037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Dufour, J.M., 1981. "Rank Tests for Serial Dependence," Cahiers de recherche 8127, Universite de Montreal, Departement de sciences economiques.
  12. Hallin, M. & Puri, M.L., 1992. "Rank Tests for Time Series Analysis , A Survey," Papers 9210, Universite Libre de Bruxelles - C.E.M.E..
  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. 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.
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