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A non-parametric independence test using permutation entropy

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  • Matilla-Garci­a, Mariano
  • Ruiz Mari­n, Manuel

Abstract

In the present paper we construct a new, simple, consistent and powerful test for independence by using symbolic dynamics and permutation entropy as a measure of serial dependence. We also give a standard asymptotic distribution of an affine transformation of the permutation entropy under the null hypothesis of independence. The test statistic and its standard limit distribution are invariant to any monotonic transformation. The test applies to time series with discrete or continuous distributions. Eventhough the test is based on entropy measures, it avoids smoothed non-parametric estimation. An application to several daily financial time series illustrates our approach.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:139-155
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    References listed on IDEAS

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    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    3. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 437-453.
    4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    5. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
    6. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    7. 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.
    8. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
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    Citations

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    Cited by:

    1. Jesus Mur & Marcos Herrera & Manuel Ruiz, 2011. "Selecting the W Matrix. Parametric vs Nonparametric Approaches," ERSA conference papers ersa11p1055, European Regional Science Association.
    2. López, Fernando & Matilla-García, Mariano & Mur, Jesús & Marín, Manuel Ruiz, 2010. "A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 40(2-3), pages 106-115, May.
    3. Richard Harris & John Moffat & Victoria Kravtsova, 2011. "In Search of ‘ W ’," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(3), pages 249-270, February.
    4. Matilla-García, Mariano & Ruiz Marín, Manuel, 2009. "Detection of non-linear structure in time series," Economics Letters, Elsevier, vol. 105(1), pages 1-6, October.
    5. repec:eee:ecolet:v:161:y:2017:i:c:p:5-9 is not listed on IDEAS
    6. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús, 2014. "Testing Spatial Causality in Cross-section Data," MPRA Paper 56678, University Library of Munich, Germany.
    7. Sensoy, Ahmet & Aras, Guler & Hacihasanoglu, Erk, 2015. "Predictability dynamics of Islamic and conventional equity markets," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 222-248.
    8. Helmut Elsinger, 2010. "Independence Tests based on Symbolic Dynamics," Working Papers 165, Oesterreichische Nationalbank (Austrian Central Bank).
    9. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2011. "¿Cuál matriz de pesos espaciales?. Un enfoque sobre selección de modelos
      [Which spatial weighting matrix? An approach for model selection]
      ," MPRA Paper 37585, University Library of Munich, Germany.
    10. Elsinger, Helmut, 2013. "Comment on: A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 131-138.
    11. Marcos Herrera & Manuel Ruiz & Jesús Mur, 2013. "Detecting Dependence Between Spatial Processes," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(4), pages 469-497, February.
    12. Elsinger, Helmut, 2013. "Comment on: A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 838-840.
    13. Mariano Matilla-García & Manuel Ruiz Marín & Mohammed Dore & Rina Ojeda, 2014. "Nonparametric correlation integral–based tests for linear and nonlinear stochastic processes," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 181-193, April.
    14. Herrera Gómez, Marcos, 2010. "Causalidad Espacial. Enfoque No Paramétrico
      [Spatial Causality. Non-Parametric Approach]
      ," MPRA Paper 61326, University Library of Munich, Germany.
    15. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús, 2011. "Detección de Dependencia Espacial mediante Análisis Simbólico
      [Detection of Spatial Dependence using Symbolic Analysis]
      ," MPRA Paper 38603, University Library of Munich, Germany.
    16. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2012. "Selecting the Most Adequate Spatial Weighting Matrix:A Study on Criteria," MPRA Paper 73700, University Library of Munich, Germany.
    17. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús & Paelinck, Jean, 2010. "A Non-Parametric Approach to Spatial Causality," MPRA Paper 36768, University Library of Munich, Germany.
    18. Yoon, Gawon, 2010. "Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?," Economic Modelling, Elsevier, vol. 27(2), pages 605-612, March.
    19. Jesus Mur & Antonio Paez, 2011. "Local weighting or the necessity of flexibility," ERSA conference papers ersa11p942, European Regional Science Association.

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