IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v144y2008i1p139-155.html
   My bibliography  Save this article

A non-parametric independence test using permutation entropy

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(08)00002-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Yongmiao Hong, 1998. "Testing for pairwise serial independence via the empirical distribution function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 429-453.
    4. 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.
    5. 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.
    6. Clive Granger & Jin‐Lung Lin, 1994. "Using The Mutual Information Coefficient To Identify Lags In Nonlinear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 371-384, July.
    7. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
    8. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 437-453.
    9. Miguel A. Delgado, 1996. "Testing Serial Independence Using The Sample Distribution Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 271-285, May.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    2. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Testing Serial Independence via Density-Based Measures of Divergence," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 627-641, September.
    3. repec:wyi:journl:002087 is not listed on IDEAS
    4. Yongmiao Hong & Xia Wang & Wenjie Zhang & Shouyang Wang, 2017. "An efficient integrated nonparametric entropy estimator of serial dependence," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 728-780, October.
    5. Diks Cees & Manzan Sebastiano, 2002. "Tests for Serial Independence and Linearity Based on Correlation Integrals," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(2), pages 1-22, July.
    6. Yongmiao Hong, 2013. "Serial Correlation and Serial Dependence," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    7. 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.
    8. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.
    9. Neshat Beheshti & Jeffrey S. Racine & Ehsan S. Soofi, 2015. "Information Measures for Nonparametric Kernel Estimation," Department of Economics Working Papers 2015-03, McMaster University.
    10. Cho, Jin Seo & White, Halbert, 2011. "Generalized runs tests for the IID hypothesis," Journal of Econometrics, Elsevier, vol. 162(2), pages 326-344, June.
    11. Cees Diks & Sebastiano Manzan, 2001. "Tests for Serial Independence and Linearity based on Correlation Integrals," Tinbergen Institute Discussion Papers 01-085/1, Tinbergen Institute.
    12. Arthur Lewbel, 2000. "Asymptotic Trimming for Bounded Density Plug-in Estimators," Boston College Working Papers in Economics 479, Boston College Department of Economics, revised 30 Oct 2000.
    13. Diks Cees & Panchenko Valentyn, 2008. "Rank-based Entropy Tests for Serial Independence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-21, March.
    14. Cees Diks & Valentyn Panchenko, 2005. "Nonparametric Tests for Serial Independence Based on Quadratic Forms," Tinbergen Institute Discussion Papers 05-076/1, Tinbergen Institute.
    15. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    16. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    17. Lanh Tran & Ba Chu & Chunfeng Huang & Kim P. Huynh, 2014. "Adaptive permutation tests for serial independence," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 183-208, August.
    18. Wu, Ximing, 2010. "Exponential Series Estimator of multivariate densities," Journal of Econometrics, Elsevier, vol. 156(2), pages 354-366, June.
    19. L. Bagnato & L. De Capitani & A. Punzo, 2016. "The Kullback–Leibler autodependogram," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2574-2594, October.
    20. 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.
    21. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:144:y:2008:i:1:p:139-155. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.