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Recovering the Most Entropic Copulas from Preliminary Knowledge of Dependence

Author

Listed:
  • Ba Chu

    () (Department of Economics, Carleton University, B-857 Loeb Building, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada)

  • Stephen Satchell

    () (Trinity College, University of Cambridge, Cambridge CB2 1TQ, UK
    The University of Sydney Business School, New South Wales NSW 2006, Australia)

Abstract

This paper provides a new approach to recover relative entropy measures of contemporaneous dependence from limited information by constructing the most entropic copula (MEC) and its canonical form, namely the most entropic canonical copula (MECC). The MECC can effectively be obtained by maximizing Shannon entropy to yield a proper copula such that known dependence structures of data (e.g., measures of association) are matched to their empirical counterparts. In fact the problem of maximizing the entropy of copulas is the dual to the problem of minimizing the Kullback-Leibler cross entropy (KLCE) of joint probability densities when the marginal probability densities are fixed. Our simulation study shows that the proposed MEC estimator can potentially outperform many other copula estimators in finite samples.

Suggested Citation

  • Ba Chu & Stephen Satchell, 2016. "Recovering the Most Entropic Copulas from Preliminary Knowledge of Dependence," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-21, March.
  • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:2:p:20-:d:66662
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    References listed on IDEAS

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    More about this item

    Keywords

    entropy; relative entropy measure of joint dependence; copula; most entropic copula; canonical; kullback-Leibler cross entropy;

    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

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