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Stochastic hyperplane-based ranks and their use in multivariate portmanteau tests

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  • Hudecová, Šárka
  • Šiman, Miroslav

Abstract

The article proposes and justifies an optimal rank-based portmanteau test of multivariate elliptical strict white noise against multivariate serial dependence. It is based on new stochastic hyperplane-based ranks that are simpler and easier to compute than other usable hyperplane-based competitors and still share with them many good properties such as their distribution-free nature, affine invariance, efficiency, robustness and weak moment assumptions. The finite-sample performance of the portmanteau test is illustrated empirically in a small Monte Carlo simulation study.

Suggested Citation

  • Hudecová, Šárka & Šiman, Miroslav, 2024. "Stochastic hyperplane-based ranks and their use in multivariate portmanteau tests," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:jmvana:v:204:y:2024:i:c:s0047259x24000514
    DOI: 10.1016/j.jmva.2024.105344
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    References listed on IDEAS

    as
    1. Hudecová, Šárka & Šiman, Miroslav, 2022. "Multivariate ranks based on randomized lift-interdirections," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    2. Marc. Hallin & Jean‐François Ingenbleek & Madan L. Puri, 1987. "Linear And Quadratic Serial Rank Tests For Randomness Against Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(4), pages 409-424, July.
    3. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
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    5. Jean‐Marie Dufour, 1981. "Rank Tests For Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(3), pages 117-128, May.
    6. 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.
    7. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
    8. Šárka Hudecová & Jana Klicnarová & Miroslav Šiman, 2020. "Incomplete interdirections and lift-interdirections," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(1), pages 93-108, January.
    9. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    10. Paindaveine, Davy, 2009. "On Multivariate Runs Tests for Randomness," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1525-1538.
    11. Dufour, J.M., 1979. "Rank Tests for Serial Dependence," Cahiers de recherche 7815, Universite de Montreal, Departement de sciences economiques.
    12. Marc Hallin & Guy Melard, 1988. "Rank-based tests for randomness against first-order serial dependence," ULB Institutional Repository 2013/2015, ULB -- Universite Libre de Bruxelles.
    13. Sun, Changyou & Liao, Xianchun, 2011. "Effects of litigation under the Endangered Species Act on forest firm values," Journal of Forest Economics, Elsevier, vol. 17(4), pages 388-398.
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