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Asymptotically most powerful rank tests for multivariate randomness against serial dependence

Author

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  • Hallin, Marc
  • Ingenbleek, Jean-Francois
  • Puri, Madan L.

Abstract

A class of linear serial multirank statistics is introduced for the problem of testing the null hypothesis that a multivariate series of observations is white noise (with unspecified density function) against alternatives of ARMA dependence. The asymptotic distributional properties of these statistics are investigated, both under the null as well as local alternative hypotheses. These statistics are shown to provide permutationally distribution-free tests that are asymptotically most powerful against specified local alternatives of ARMA dependence. In particular, a test of the van der Waerden type is shown to be asymptotically as powerful as the corresponding normal theory parametric test, based on classical sample autocovariances.

Suggested Citation

  • Hallin, Marc & Ingenbleek, Jean-Francois & Puri, Madan L., 1989. "Asymptotically most powerful rank tests for multivariate randomness against serial dependence," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 34-71, July.
    • Handle: RePEc:eee:jmvana:v:30:y:1989:i:1:p:34-71
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    Cited by:

    1. Christian Genest, 2024. "A Conversation With Marc Hallin," International Statistical Review, International Statistical Institute, vol. 92(2), pages 137-159, August.
    2. 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.
    3. 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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