IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/05-2005.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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).

Suggested Citation

  • 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.
    • Handle: RePEc:mtl:montec:05-2005
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/05-2005-cah.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Robert J. Gordon, 1986. "The American Business Cycle: Continuity and Change," NBER Books, National Bureau of Economic Research, Inc, number gord86-1.
    3. Dufour, J.M., 1988. "Non-Uniform Bounds for Nonparametric T Tests," Cahiers de recherche 8820, Universite de Montreal, Departement de sciences economiques.
    4. Dufour, Jean-Marie & Farhat, Abdeljelil & Hallin, Marc, 2006. "Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 123-142, January.
    5. 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.
    6. 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 151-173, February.
    7. 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.
    8. 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.
    9. Dufour, Jean-Marie & Hallin, Marc, 1991. "Nonuniform Bounds for Nonparametric t-Tests," Econometric Theory, Cambridge University Press, vol. 7(2), pages 253-263, June.
    10. Jean‐Marie Dufour, 1981. "Rank Tests For Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(3), pages 117-128, May.
    11. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    12. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-494, March.
    13. Dufour, J-M. & Hallin, M., 1990. "Improved Eaton Bounds for Linear Combinations of Bounded Random Variables , with Statistical Applications," Papers 9104, Universite Libre de Bruxelles - C.E.M.E..
    14. Dufour, J.M., 1979. "Rank Tests for Serial Dependence," Cahiers de recherche 7815, Universite de Montreal, Departement de sciences economiques.
    15. Marc Hallin & Madan Lal Puri, 1992. "Rank tests for time-series analysis: a survey," ULB Institutional Repository 2013/2229, ULB -- Universite Libre de Bruxelles.
    16. 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.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dufour, Jean-Marie & Farhat, Abdeljelil & Hallin, Marc, 2006. "Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 123-142, January.
    2. Christopher Malikane & Tshepo Mokoka, 2014. "The new Keynesian Phillips curve: endogeneity and misspecification," Applied Economics, Taylor & Francis Journals, vol. 46(25), pages 3082-3089, September.
    3. Aguilar, Mike & Hill, Jonathan B., 2015. "Robust score and portmanteau tests of volatility spillover," Journal of Econometrics, Elsevier, vol. 184(1), pages 37-61.
    4. Tuvaandorj, Purevdorj, 2020. "Regression discontinuity designs, white noise models, and minimax," Journal of Econometrics, Elsevier, vol. 218(2), pages 587-608.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2532-2553, November.
    2. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    3. 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.
    4. Luger, Richard, 2003. "Exact non-parametric tests for a random walk with unknown drift under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 115(2), pages 259-276, August.
    5. Dufour, Jean-Marie, 2008. "Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms," UC3M Working papers. Economics we086027, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Tuvaandorj, Purevdorj, 2020. "Regression discontinuity designs, white noise models, and minimax," Journal of Econometrics, Elsevier, vol. 218(2), pages 587-608.
    7. Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 173-191, Springer.
    8. Elise Coudin & Jean-Marie Dufour, 2017. "Finite-sample generalized confidence distributions and sign-based robust estimators in median regressions with heterogenous dependent errors," CIRANO Working Papers 2017s-06, CIRANO.
    9. Bryan Campbell & Eric Ghysels, 1997. "An Empirical Analysis of the Canadian Budget Process," Canadian Journal of Economics, Canadian Economics Association, vol. 30(3), pages 553-576, August.
    10. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    11. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    12. Touhami Abdelkhalek & Jean-Marie Dufour, 1998. "Statistical Inference For Computable General Equilibrium Models, With Application To A Model Of The Moroccan Economy," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 520-534, November.
    13. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
    14. Firmin Doko Tchatoka & Lauren Slinger & Virginie Masson, 2020. "Revisiting empirical studies on the liquidity effect: An identication-robust approach," School of Economics and Public Policy Working Papers 2020-02, University of Adelaide, School of Economics and Public Policy.
    15. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
    16. Elise Coudin & Jean-Marie Dufour, 2010. "Finite and Large Sample Distribution-Free Inference in Median Regressions with Instrumental Variables," Working Papers 2010-56, Center for Research in Economics and Statistics.
    17. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Discussion Paper 2003-23, Tilburg University, Center for Economic Research.
    18. Sermin Gungor & Richard Luger, 2016. "Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 161-175, April.
    19. Fu, Hsuan & Luger, Richard, 2022. "Multiple testing of the forward rate unbiasedness hypothesis across currencies," Journal of Empirical Finance, Elsevier, vol. 68(C), pages 232-245.
    20. Firmin Doko Tchatoka & Jean‐Marie Dufour, 2014. "Identification‐robust inference for endogeneity parameters in linear structural models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 165-187, February.

    More about this item

    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;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montec:05-2005. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.