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An independence test based on recurrence rates

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  • Kalemkerian, Juan
  • Fernández, Diego

Abstract

A new test of independence between random elements is presented in this article. The test is based on a functional of the Cramér–von Mises type, which is applied to a U-process that is defined from the recurrence rates. Theorems of asymptotic distribution under H0, and consistency under a wide class of alternatives are obtained. The results under contiguous alternatives are also shown. The test has very good behavior under several alternatives, when compared to other tests that are widely used in literature. In addition, the new test could be used for discrete or continuous time series.

Suggested Citation

  • Kalemkerian, Juan & Fernández, Diego, 2020. "An independence test based on recurrence rates," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:jmvana:v:178:y:2020:i:c:s0047259x19301198
    DOI: 10.1016/j.jmva.2020.104624
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    References listed on IDEAS

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    1. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    2. Bakirov, Nail K. & Rizzo, Maria L. & Szekely, Gábor J., 2006. "A multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1742-1756, September.
    3. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    4. Kojadinovic, Ivan & Holmes, Mark, 2009. "Tests of independence among continuous random vectors based on Cramr-von Mises functionals of the empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1137-1154, July.
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