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A multivariate Wald-Wolfowitz rank test against serial dependence

Marc Hallin () and Madan Lal Puri

ULB Institutional Repository from ULB -- Universite Libre de Bruxelles

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.

Date: 1995-03
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Published in: Canadian Journal of Statistics (1995) v.23 n° 1,p.55-65

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