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Center-outward Rank- and Sign-based VARMA Portmanteau Tests

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  • Marc Hallin
  • Hang Liu

Abstract

Revisiting the pseudo-Gaussian tests of Chitturi (1974), Hosking (1980), and Li and McLeod (1981) for VARMA models from a Le Cam perspective, we first provide a more precise and rigorous description of the asymptotic behavior of the multivariate portmanteau test statistic.Then, based on the concepts of center-outward ranks and signs recently developed in Hallin et al. (2021), we propose a class of multivariateportmanteau rank- and sign-based test statistics which, under the null hypothesis and under a broad family of innovation densities, can be approximated by an asymptotically chi-square variable. The asymptotic properties of these tests are derived; simulations demonstratetheir advantages over their classical pseudo-Gaussian counterpart.

Suggested Citation

  • Marc Hallin & Hang Liu, 2022. "Center-outward Rank- and Sign-based VARMA Portmanteau Tests," Working Papers ECARES 2022-27, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/349259
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    References listed on IDEAS

    as
    1. Eustasio del Barrio & Alberto González-Sanz & Marc Hallin, 2022. "Nonparametric Multiple-Output Center-Outward Quantile Regression," Working Papers ECARES 2022-10, ULB -- Universite Libre de Bruxelles.
    2. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    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.
    4. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    5. del Barrio, Eustasio & González-Sanz, Alberto & Hallin, Marc, 2020. "A note on the regularity of optimal-transport-based center-outward distribution and quantile functions," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    6. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multivariate ranks and signs; Measure transportation; Distributionfreeness; Le Cam’s asymptotic theory; Multivariate time series;
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