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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

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    1. Eustasio del Barrio & Alberto González Sanz & Marc Hallin, 2025. "Nonparametric Multiple-Output Center-Outward Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 120(550), pages 818-832, April.
    2. repec:spo:wpmain: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. 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).
    5. 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.
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