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Out-of-sample comparison of copula specifications in multivariate density forecasts

Author

Listed:
  • Cees Diks

    () (University of Amsterdam)

  • Valentyn Panchenko

    () (School of Economics, University of New South Wales)

  • Dick van Dijk

    () (Econometric Institute, Erasmus University Rotterdam)

Abstract

We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or nonnested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student’s t copula is favored over Gaussian, Gumbel and Clayton copulas. This suggests that these exchange rate returns are characterized by symmetric tail dependence.

Suggested Citation

  • Cees Diks & Valentyn Panchenko & Dick van Dijk, 2008. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Discussion Papers 2008-23, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2008-23
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    File URL: http://wwwdocs.fce.unsw.edu.au/economics/Research/WorkingPapers/2008_23.pdf
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    References listed on IDEAS

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    3. Tranberg, Bo & Hansen, Rasmus Thrane & Catania, Leopoldo, 2020. "Managing volumetric risk of long-term power purchase agreements," Energy Economics, Elsevier, vol. 85(C).
    4. Cees Diks & Valentyn Panchenko & Oleg Sokolinskiy, & Dick van Dijk, 2013. "Comparing the Accuracy of Copula-Based Multivariate Density Forecasts in Selected Regions of Support," Tinbergen Institute Discussion Papers 13-061/III, Tinbergen Institute.
    5. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    6. Marc Gronwald & Janina Ketterer & Stefan Trück, 2011. "The Dependence Structure between Carbon Emission Allowances and Financial Markets - A Copula Analysis," CESifo Working Paper Series 3418, CESifo.
    7. Liu, Xiaochun, 2015. "Modeling time-varying skewness via decomposition for out-of-sample forecast," International Journal of Forecasting, Elsevier, vol. 31(2), pages 296-311.
    8. Diks, Cees & Panchenko, Valentyn & Sokolinskiy, Oleg & van Dijk, Dick, 2014. "Comparing the accuracy of multivariate density forecasts in selected regions of the copula support," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 79-94.
    9. Avdulaj, Krenar & Barunik, Jozef, 2015. "Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data," Energy Economics, Elsevier, vol. 51(C), pages 31-44.
    10. Hayette Gatfaoui, 2010. "Investigating the dependence structure between credit default swap spreads and the U.S. financial market," Annals of Finance, Springer, vol. 6(4), pages 511-535, October.
    11. Kiss, Tamás & Nguyen, Hoang & Österholm, Pär, 2020. "Modelling Returns in US Housing Prices – You’re the One for Me, Fat Tails," Working Papers 2020:13, Örebro University, School of Business.
    12. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    13. Weiß, Gregor N.F., 2011. "Are Copula-GoF-tests of any practical use? Empirical evidence for stocks, commodities and FX futures," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(2), pages 173-188, May.
    14. Abdallah Ben Saida & Jean-luc Prigent, 2018. "On the robustness of portfolio allocation under copula misspecification," Annals of Operations Research, Springer, vol. 262(2), pages 631-652, March.
    15. 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.
    16. Gang-Jin Wang & Chi Xie & Peng Zhang & Feng Han & Shou Chen, 2014. "Dynamics of Foreign Exchange Networks: A Time-Varying Copula Approach," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-11, May.
    17. Diks, Cees & Fang, Hao, 2020. "Comparing density forecasts in a risk management context," International Journal of Forecasting, Elsevier, vol. 36(2), pages 531-551.
    18. Anufriev, Mikhail & Panchenko, Valentyn, 2015. "Connecting the dots: Econometric methods for uncovering networks with an application to the Australian financial institutions," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 241-255.
    19. Balaev, Alexey, 2014. "The copula based on multivariate t-distribution with vector of degrees of freedom," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 90-110.
    20. Fawad, Muhammad & Yan, Ting & Chen, Lu & Huang, Kangdi & Singh, Vijay P., 2019. "Multiparameter probability distributions for at-site frequency analysis of annual maximum wind speed with L-Moments for parameter estimation," Energy, Elsevier, vol. 181(C), pages 724-737.
    21. Pelster, Matthias & Vilsmeier, Johannes, 2016. "The determinants of CDS spreads: Evidence from the model space," Discussion Papers 43/2016, Deutsche Bundesbank.
    22. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.

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    More about this item

    Keywords

    Copula-based density forecast; semiparametric statistics; out-of-sample forecast evaluation; Kullback-Leibler Information Criterion; empirical copula;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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