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Rank-Based Testing for Semiparametric VAR Models: a measure transportation approach


  • Marc Hallin
  • Davide La Vecchia
  • Hang Liu


We develop a class of tests for semiparametric vector autoregressive (VAR) models with unspecified innovation densities, based on the recent measure-transportation-based concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam's asymptotic theory of statistical experiments, yield novel testing procedures, which (a) are valid under a broad class of innovation densities (possibly non-elliptical, skewed, and/or with infinite moments), (b) are optimal (locally asymptotically maximin or most stringent) at selected ones, and (c) are robust against additive outliers. In order to do so, we establish a Hajek asymptotic representation result, of independent interest, for a general class of center-outward rank-based serial statistics. As an illustration, we consider the problems of testing the absence of serial correlation in multiple-output and possibly non-linear regression (an extension of the classical Durbin-Watson problem) and the sequential identification of the order p of a vector autoregressive (VAR(p)) model. A Monte Carlo comparative study of our tests and their routinely-applied Gaussian competitors demonstrates the benefits (in terms of size, power, and robustness) of our methodology; these benefits are particularly significant in the presence of asymmetric and leptokurtic innovation densities. A real data application concludes the paper.

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  • Marc Hallin & Davide La Vecchia & Hang Liu, 2020. "Rank-Based Testing for Semiparametric VAR Models: a measure transportation approach," Working Papers ECARES 2020-47, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/314257

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    References listed on IDEAS

    1. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434,, revised Sep 2015.
    3. Marc Hallin & Youssef Benghabrit, 1996. "Rank-based tests for autoregressive against bilinear serial dependence," ULB Institutional Repository 2013/2057, ULB -- Universite Libre de Bruxelles.
    4. 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.
    5. Marc Hallin & Youssef Benghabrit, 1992. "Optimal rank-based tests against first-order superdiagonal bilinear dependence," ULB Institutional Repository 2013/2039, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. Marc Hallin & Hongjian Shi & Mathias Drton & Fang Han, 2021. "Center-Outward Sign- and Rank-Based Quadrant, Spearman, and Kendall Tests for Multivariate Independence," Working Papers ECARES 2021-27, ULB -- Universite Libre de Bruxelles.

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    More about this item


    Multivariate ranks; Distribution-freeness; Hájek representation; Local asymptotic normality; Durbin-Watson; VAR order identification;
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