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A symbolic test for testing independence between time series

Author

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  • Mariano Matilla‐García
  • José Miguel Rodríguez
  • Manuel Ruiz Marín

Abstract

In this article we introduce a test for independence between two processes {Xt} and {Yt}. To this end we rely on symbolic dynamics and permutation entropy as a measure of dependence. As a result, a nonparametric (model‐free) test for either linear or nonlinear processes is presented. The test is consistent for a broad range of dependent alternatives. Empirical simulations indicate and highlight the general utility of the test for time‐series analysts.

Suggested Citation

  • Mariano Matilla‐García & José Miguel Rodríguez & Manuel Ruiz Marín, 2010. "A symbolic test for testing independence between time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 76-85, March.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:2:p:76-85
    DOI: 10.1111/j.1467-9892.2009.00645.x
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    References listed on IDEAS

    as
    1. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
    2. Dinh Tuan Pham & Roch Roy & Lyne Cédras, 2003. "Tests for non‐correlation of two cointegrated ARMA time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 553-577, September.
    3. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
    4. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
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    1. repec:onb:oenbwp:y::i:165:b:1 is not listed on IDEAS
    2. Helmut Elsinger, 2010. "Independence Tests based on Symbolic Dynamics," Working Papers 165, Oesterreichische Nationalbank (Austrian Central Bank).
    3. Matilla-García, Mariano & Marín, Manuel Ruiz & Dore, Mohammed I., 2014. "A permutation entropy based test for causality: The volume–stock price relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 280-288.
    4. Weiß, Christian H. & Ruiz Marín, Manuel & Keller, Karsten & Matilla-García, Mariano, 2022. "Non-parametric analysis of serial dependence in time series using ordinal patterns," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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