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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.

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File URL: http://www.sciencedirect.com/science/article/B6VC0-4RM7N3M-1/1/403fe1ec8502aa8065c71615a8f918fc
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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 144 (2008)
Issue (Month): 1 (May)
Pages: 139-155

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Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:139-155

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  2. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer, vol. 41(4), pages 683-697, December.
  3. Mototsugu Shintani & Oliver Linton, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," Vanderbilt University Department of Economics Working Papers 0309, Vanderbilt University Department of Economics.
  4. 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, 09.
  5. 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.
  6. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
  7. 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.
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Citations

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Cited by:
  1. Marcos Herrera & Manuel Ruiz & Jes�s Mur, 2013. "Detecting Dependence Between Spatial Processes," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(4), pages 469-497, February.
  2. 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.
  3. 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.
  4. 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.
  5. Jesus Mur & Marcos Herrera & Manuel Ruiz, 2011. "Selecting the W Matrix. Parametric vs Nonparametric Approaches," ERSA conference papers ersa11p1055, European Regional Science Association.
  6. Jesus Mur & Antonio Paez, 2011. "Local weighting or the necessity of flexibility," ERSA conference papers ersa11p942, European Regional Science Association.
  7. 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.
  8. 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.
  9. Helmut Elsinger, 2010. "Independence Tests based on Symbolic Dynamics," Working Papers 165, Oesterreichische Nationalbank (Austrian Central Bank).
  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. 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.
  12. 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.

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