IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-314257.html
   My bibliography  Save this paper

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

Author

Listed:
  • Marc Hallin
  • Davide La Vecchia
  • Hang Liu

Abstract

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/314257/3/2020-47-HALLIN_LAVECCHIA_LIU-rank-based.pdf
    File Function: Full text for the whole work, or for a work part
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marc Hallin & Davide La Vecchia & H Liu, 2019. "Center-Outward R-Estimation for Semiparametric VARMA Models," Working Papers ECARES 2019-25, ULB -- Universite Libre de Bruxelles.
    2. Marc Hallin & Hang Liu, 2022. "Center-outward Rank- and Sign-based VARMA Portmanteau Tests," Working Papers ECARES 2022-27, ULB -- Universite Libre de Bruxelles.
    3. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    4. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    5. María Edo & Walter Sosa Escudero & Marcela Svarc, 2021. "A multidimensional approach to measuring the middle class," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(1), pages 139-162, March.
    6. Faugeras, Olivier P. & Rüschendorf, Ludger, 2021. "Functional, randomized and smoothed multivariate quantile regions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    7. Marc Hallin & Gilles Mordant, 2021. "On the Finite-Sample Performance of Measure Transportation-Based Multivariate Rank Tests," Working Papers ECARES 2021-24, ULB -- Universite Libre de Bruxelles.
    8. Jonas Meier, 2020. "Multivariate Distribution Regression," Diskussionsschriften dp2023, Universitaet Bern, Departement Volkswirtschaft.
    9. Alfred Galichon & Bernard Salani'e, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Papers 2106.02371, arXiv.org.
    10. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    11. Davy Paindaveine & Germain Van Bever, 2017. "Halfspace Depths for Scatter, Concentration and Shape Matrices," Working Papers ECARES ECARES 2017-19, ULB -- Universite Libre de Bruxelles.
    12. Marc Hallin & Daniel Hlubinka & Sarka Hudecova, 2021. "Efficient Fully Distribution-Free Center-Outward Rank Tests for Multiple-Output Regression and MANOVA," Working Papers ECARES 2021-13, ULB -- Universite Libre de Bruxelles.
    13. Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    14. Petra Laketa & Stanislav Nagy, 2022. "Halfspace depth for general measures: the ray basis theorem and its consequences," Statistical Papers, Springer, vol. 63(3), pages 849-883, June.
    15. Hongjian Shi & Marc Hallin & Mathias Drton & Fang Han, 2020. "Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs," Working Papers ECARES 2020-23, ULB -- Universite Libre de Bruxelles.
    16. 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.
    17. Beirlant, J. & Buitendag, S. & del Barrio, E. & Hallin, M. & Kamper, F., 2020. "Center-outward quantiles and the measurement of multivariate risk," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 79-100.
    18. Manuel Arellano & Stéphane Bonhomme, 2019. "Recovering Latent Variables by Matching," Working Papers wp2019_1914, CEMFI.
    19. Florian Gunsilius & Susanne M. Schennach, 2019. "Independent nonlinear component analysis," CeMMAP working papers CWP46/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Hudecová, Šárka & Šiman, Miroslav, 2022. "Multivariate ranks based on randomized lift-interdirections," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eca:wpaper:2013/314257. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/arulbbe.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/arulbbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.