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Derivatives and Fisher information of bivariate copulas

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  • Ulf Schepsmeier
  • Jakob Stöber

Abstract

Data sets with complex relationships between random variables are increasingly studied in statistical applications. A popular approach to model their dependence is the use of copula functions. Our contribution is to derive expressions for the observed and expected information for several bivariate copula families, in particular for the Student’s $$t$$ -copula. Further likelihood derivatives which are required for numerical implementations are computed and a numerically stable implementation is provided in the R-package VineCopula. Using a real world data set of stock returns, we demonstrate the applicability of our approach for the routinely calculation of standard errors. In particular, we illustrate how this prevents overestimating the time-variation of dependence parameters in a rolling window analysis. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:525-542
    DOI: 10.1007/s00362-013-0498-x
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    Cited by:

    1. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    2. Ackerer Damien & Vatter Thibault, 2017. "Dependent defaults and losses with factor copula models," Dependence Modeling, De Gruyter, vol. 5(1), pages 375-399, December.
    3. Nguyen, Hoang & Ausín, M. Concepción & Galeano, Pedro, 2020. "Variational inference for high dimensional structured factor copulas," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    4. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    5. Matthieu Garcin & Maxime L. D. Nicolas, 2021. "Nonparametric estimator of the tail dependence coefficient: balancing bias and variance," Papers 2111.11128, arXiv.org, revised Jul 2023.
    6. Stöber, Jakob & Hong, Hyokyoung Grace & Czado, Claudia & Ghosh, Pulak, 2015. "Comorbidity of chronic diseases in the elderly: Patterns identified by a copula design for mixed responses," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 28-39.
    7. O. Chatrabgoun & G. Parham & R. Chinipardaz, 2017. "A Legendre multiwavelets approach to copula density estimation," Statistical Papers, Springer, vol. 58(3), pages 673-690, September.
    8. Pircalabu, A. & Hvolby, T. & Jung, J. & Høg, E., 2017. "Joint price and volumetric risk in wind power trading: A copula approach," Energy Economics, Elsevier, vol. 62(C), pages 139-154.
    9. Kreuzer, Alexander & Czado, Claudia, 2021. "Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 130-150.
    10. Schepsmeier, Ulf, 2015. "Efficient information based goodness-of-fit tests for vine copula models with fixed margins: A comprehensive review," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 34-52.
    11. Siem Jan Koopman & Rutger Lit & André Lucas, 2015. "Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions," Tinbergen Institute Discussion Papers 15-037/III/DSF90, Tinbergen Institute.
    12. Schmidt, Rouven & Kneib, Thomas, 2023. "Multivariate distributional stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    13. Hirofumi Michimae & Takeshi Emura, 2022. "Bayesian ridge estimators based on copula-based joint prior distributions for regression coefficients," Computational Statistics, Springer, vol. 37(5), pages 2741-2769, November.
    14. Elizabeth D. Schifano & Himchan Jeong & Ved Deshpande & Dipak K. Dey, 2021. "Fully and empirical Bayes approaches to estimating copula-based models for bivariate mixed outcomes using Hamiltonian Monte Carlo," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 133-152, March.
    15. Hyun Jin Jang & Kiseop Lee & Kyungsub Lee, 2020. "Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 247-275, February.
    16. repec:cte:wsrepe:27652 is not listed on IDEAS
    17. Damien Ackerer & Thibault Vatter, 2016. "Dependent Defaults and Losses with Factor Copula Models," Papers 1610.03050, arXiv.org, revised Jan 2018.

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