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Kendall's tau for serial dependence

Author

Listed:
  • Marc Hallin
  • Thomas S. Ferguson
  • Christian Genest

Abstract

The authors show how Kendall's tau can be adapted to test against serial dependence in a univariate time series context. They provide formulas for the mean and variance of circular and noncircular versions of this statistic, and they prove its asymptotic normality under the hypothesis of independence. They present also a Monte Carlo study comparing the power and size of a test based on Kendall's tau with the power and size of competing procedures based on alternative parametric and nonparametric measures of serial dependence. In particular, their simulations indicate that Kendall's tau outperforms Spearman's rho in detecting first-order autoregressive dependence, despite the fact that these two statistics are asymptotically equivalent under the null hypothesis, as well as under local alternatives.

Suggested Citation

  • Marc Hallin & Thomas S. Ferguson & Christian Genest, 2000. "Kendall's tau for serial dependence," ULB Institutional Repository 2013/2093, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/2093
    Note: FLWIN
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    Citations

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    Cited by:

    1. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
    2. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2016. "Stat Trek," Dependence Modeling, De Gruyter, vol. 4(1), pages 109-122, May.
    3. Marc Hallin & Yvik Swan & Thomas Verdebout, 2013. "A Serial Version of Hodges and Lehmann's "6/pi Result"," Working Papers ECARES ECARES 2013-17, ULB -- Universite Libre de Bruxelles.
    4. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    5. Lin, N. & Xi, R., 2010. "Fast surrogates of U-statistics," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 16-24, January.
    6. Yan Ma, 2012. "On inference for Kendall's τ within a longitudinal data setting," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2441-2452, July.
    7. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. II," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 23(3), pages 98-132.
    8. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Emura, Takeshi & Lai, Ching-Chieh & Sun, Li-Hsien, 2023. "Change point estimation under a copula-based Markov chain model for binomial time series," Econometrics and Statistics, Elsevier, vol. 28(C), pages 120-137.
    10. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
    11. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.

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