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Testing the constancy of Spearman’s rho in multivariate time series

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Abstract

A class of tests for change-point detection designed to be particularly sensitive to changes in the cross-sectional rank correlation of multivariate time series is proposed. The derived procedures are based on several multivariate extensions of Spearman’s rho. Two approaches to carry out the tests are studied: the first one is based on resampling and the second one consists of estimating the asymptotic null distribution. The asymptotic validity of both techniques is proved under the null for strongly mixing observations. A procedure for estimating a key bandwidth parameter involved in both approaches is proposed, making the derived tests parameter-free. Their finite-sample behavior is investigated through Monte Carlo experiments. Practical recommendations are made and an illustration on trivariate financial data is finally presented.

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Acknowledgments

The authors are grateful to Axel Bücher and Johan Segers for fruitful discussions on related projects that led to improvements in this one.

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Authors and Affiliations

  1. Laboratoire de mathématiques et applications, UMR CNRS 5142, Université de Pau et des Pays de l’Adour, B.P. 1155, 64013, Pau Cedex, France

    Ivan Kojadinovic

  2. Département de mathématiques et d’informatique, Université du Québec à Trois-Rivières, C.P. 500, Trois-Rivières, QC, G9A 5H7, Canada

    Jean-François Quessy

  3. Laboratoire de mathématiques Jean Leray, Université de Nantes, B.P. 92208, 44322, Nantes Cedex 3, France

    Tom Rohmer

Authors
  1. Ivan Kojadinovic
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  2. Jean-François Quessy
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  3. Tom Rohmer
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Correspondence to Ivan Kojadinovic.

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Kojadinovic, I., Quessy, JF. & Rohmer, T. Testing the constancy of Spearman’s rho in multivariate time series. Ann Inst Stat Math 68, 929–954 (2016). https://doi.org/10.1007/s10463-015-0520-2

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  • DOI: https://doi.org/10.1007/s10463-015-0520-2

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