an:00769887
Zbl 0821.62022
Hallin, Marc; Puri, Madan L.
A multivariate Wald-Wolfowitz rank test against serial dependence
EN
Can. J. Stat. 23, No. 1, 55-65 (1995).
00026557
1995
j
62G10 62M10 62H15 62E20 62H10
Wald-Wolfowitz rank test; rank cross-covariance matrix; multivariate ARMA models; multivariate portmanteau test; multivariate model identification; rank-based cross-covariance matrices; rank autocorrelation coefficients; permutational central limit theorem; contiguous alternatives; ARMA dependence; rank-based, permutationallly distribution-free test; asymptotic local power
Summary: Rank-based cross-covariance matrices, extending to the case of multivariate observed series the (univariate) rank autocorrelation coefficients introduced by \textit{A. Wald} and \textit{J. Wolfowitz} [Ann. Math. Stat. 14, 378-388 (1943; Zbl 0060.302)], 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, permutationallly distribution-free test of the portmanteau type is derived, and its asymptotic local power is investigated. Finally, a modified rank-based version of \textit{G. C. Tiao} and \textit{G. E. P. Box}'s [J. Am. Stat. Assoc. 76, 802-816 (1981; Zbl 0483.62074)] model specification procedure is proposed, which is likely to be more reliable under non-Gaussian conditions, and more robust against gross errors.
Zbl 0060.302; Zbl 0483.62074