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A Nonparametric Test of Serial Independence for Time Series and Residuals

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  • Ghoudi, Kilani
  • Kulperger, Reg J.
  • Rémillard, Bruno

Abstract

This paper presents nonparametric tests of independence that can be used to test the independence of p random variables, serial independence for time series, or residuals data. These tests are shown to generalize the classical portmanteau statistics. Applications to both time series and regression residuals are discussed.

Suggested Citation

  • Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
    • Handle: RePEc:eee:jmvana:v:79:y:2001:i:2:p:191-218
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    References listed on IDEAS

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    1. Yongmiao Hong, 1998. "Testing for pairwise serial independence via the empirical distribution function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 429-453.
    2. Miguel A. Delgado, 1996. "Testing Serial Independence Using The Sample Distribution Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 271-285, May.
    3. Yongmiao Hong, 2000. "Generalized spectral tests for serial dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 557-574.
    4. R. J. Kulperger & R. A. Lockhart, 1998. "Tests of Independence in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 165-185, March.
    5. Barbe, Philippe & Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "On Kendall's Process," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 197-229, August.
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    4. Jean-François Quessy, 2009. "Theoretical efficiency comparisons of independence tests based on multivariate versions of Spearman’s rho," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 315-338, November.
    5. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    6. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    7. Kojadinovic, Ivan & Holmes, Mark, 2009. "Tests of independence among continuous random vectors based on Cramr-von Mises functionals of the empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1137-1154, July.
    8. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
    9. Bilodeau, M. & Lafaye de Micheaux, P., 2005. "A multivariate empirical characteristic function test of independence with normal marginals," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 345-369, August.
    10. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    11. Xiaojun Song & Haoyu Wei, 2021. "Nonparametric Tests of Conditional Independence for Time Series," Papers 2110.04847, arXiv.org.
    12. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
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    14. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Testing Serial Independence via Density-Based Measures of Divergence," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 627-641, September.
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    16. C Genest & J G Nešlehová & B Rémillard & O A Murphy, 2019. "Testing for independence in arbitrary distributions," Biometrika, Biometrika Trust, vol. 106(1), pages 47-68.
    17. Kilani Ghoudi & Bruno Rémillard, 2018. "Serial independence tests for innovations of conditional mean and variance models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 3-26, March.
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