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A multivariate Wald-Wolfowitz rank test against serial dependence

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  • Marc Hallin
  • Madan Lal Puri

Abstract

Rank-based cross-covariance matrices, extending to the case of multivariate observed series the (univariate) rank autocorrelation coefficients introduced by Wald and Wolfowitz (1943), are considered. A permutational central limit theorem is established for the joint distribution of such matrices, under the null hypothesis of (multivariate) randomness as well as under contiguous alternatives of (multivariate) ARMA dependence. A rank-based, permutationaily distribution-free test of the portmanteau type is derived, and its asymptotic local power is investigated. Finally, a modified rank-based version of Tiao and Box's model specification procedure is proposed, which is likely to be more reliable under non-Gaussian conditions, and more robust against gross errors.

Suggested Citation

  • Marc Hallin & Madan Lal Puri, 1995. "A multivariate Wald-Wolfowitz rank test against serial dependence," ULB Institutional Repository 2013/2051, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/2051
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    Cited by:

    1. Ivan Kojadinovic & Jun Yan, 2011. "Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 347-373, April.
    2. Hallin, Marc & Paindaveine, Davy, 2005. "Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 122-163, March.

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