IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v7y2019i1p10-d213039.html
   My bibliography  Save this article

Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series

Author

Listed:
  • Miguel Henry

    () (Economist at Greylock McKinnon Associates, 75 Park Plaza, 4th Floor, Boston, MA 02116, USA)

  • George Judge

    () (Graduate School and Giannini Foundation, 207 Giannini Hall, University of California Berkeley, Berkeley, CA 94720, USA)

Abstract

The focus of this paper is an information theoretic-symbolic logic approach to extract information from complex economic systems and unlock its dynamic content. Permutation Entropy (PE) is used to capture the permutation patterns-ordinal relations among the individual values of a given time series; to obtain a probability distribution of the accessible patterns; and to quantify the degree of complexity of an economic behavior system. Ordinal patterns are used to describe the intrinsic patterns, which are hidden in the dynamics of the economic system. Empirical applications involving the Dow Jones Industrial Average are presented to indicate the information recovery value and the applicability of the PE method. The results demonstrate the ability of the PE method to detect the extent of complexity (irregularity) and to discriminate and classify admissible and forbidden states.

Suggested Citation

  • Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, Open Access Journal, vol. 7(1), pages 1-16, March.
  • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:1:p:10-:d:213039
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/7/1/10/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2225-1146/7/1/10/
    Download Restriction: no

    References listed on IDEAS

    as
    1. Michael J. Stutzer, 1980. "Chaotic dynamics and bifurcation in a macro model," Staff Report 55, Federal Reserve Bank of Minneapolis.
    2. 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.
    3. Carter,Susan B. & Gartner,Scott Sigmund & Haines,Michael R. & Olmstead,Alan L. & Sutch,Richard & Wri (ed.), 2006. "The Historical Statistics of the United States 5 Volume Hardback Set," Cambridge Books, Cambridge University Press, number 9780521817912.
    4. Stutzer, Michael J., 1980. "Chaotic dynamics and bifurcation in a macro model," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 353-376, May.
    5. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521689731.
    6. repec:boc:bocode:g00016 is not listed on IDEAS
    7. Richard H. Day, 1994. "Complex Economic Dynamics - Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041413, March.
    8. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    9. repec:eee:ecolet:v:161:y:2017:i:c:p:5-9 is not listed on IDEAS
    10. J. Barkley Rosser, 1999. "On the Complexities of Complex Economic Dynamics," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 169-192, Fall.
    11. Joseph E Stiglitz, 2018. "Where modern macroeconomics went wrong," Oxford Review of Economic Policy, Oxford University Press, vol. 34(1-2), pages 70-106.
    12. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.
    13. Robert B. Barsky & J. Bradford De Long, 1993. "Why Does the Stock Market Fluctuate?," The Quarterly Journal of Economics, Oxford University Press, vol. 108(2), pages 291-311.
    14. 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.
    15. 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.
    16. Henry, Miguel & Mittelhammer, Ron & Loomis, John, 2018. "An Information-Theoretic Approach to Estimating Willingness To Pay for River Recreation Site Attributes," MPRA Paper 89842, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Cressie-Read divergence; information theoretic methods; complexity; nonparametric econometrics; permutation entropy; nonlinear time series; symbolic logic;

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C - Mathematical and Quantitative Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    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:gam:jecnmx:v:7:y:2019:i:1:p:10-:d:213039. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (XML Conversion Team). General contact details of provider: https://www.mdpi.com/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.