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LINEAR AND QUADRATIC SERIAL RANK TESTS FOR RANDOMNESS AGAINST SERIAL DEPENDENCE

Marc Hallin (), Jean‐François Ingenbleek and Madan L. Puri

Journal of Time Series Analysis, 1987, vol. 8, issue 4, 409-424

Abstract: Abstract. The problem of testing randomness against specified and unspecified contiguous ARMA alternatives is considered. In the case of specified alternative, the linear serial rank tests proposed by the authors (Hallin, Ingenbleek and Puri 1985) are shown to be asymptotically most powerful within the class of all possible tests (at the required level). In the case of unspecified alternative, however, any of the above optimal tests is unfortunately completely insensitive against a whole subclass of the alternative. Quadratic serial rank statistics, providing tests of the χ2‐type are therefore introduced. Their asymptotic distributions are derived, under the null hypothesis as well as under contiguous ARMA alternatives. The asymptotically maximin most powerful quadratic serial rank tests (for a given density) are then obtained. Because of their close similarity with the Box‐Pierce parametric test, we call them rank portmanteau tests. The asymptotic relative efficiencies (AREs) of the rank portmanteau tests with respect to one another and their AREs with respect to the corresponding Box‐Pierce and quadratic Spearman tests are derived.

Date: 1987
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https://doi.org/10.1111/j.1467-9892.1987.tb00004.x

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Working Paper: Linear and quadratic serial rank tests for randomness against serial dependence (1987)
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