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Comparing the Accuracy of Copula-Based Multivariate Density Forecasts in Selected Regions of Support

Author

Listed:
  • Cees Diks

    (University of Amsterdam, the Netherlands)

  • Valentyn Panchenko

    (University of New South Wales, Australia)

  • Oleg Sokolinskiy,

    (Rutgers Business School, United States)

  • Dick van Dijk

    (Erasmus University Rotterdam, the Netherlands)

Abstract

This discussion paper resulted in a publication in the 'Journal of Economic Dynamics and Control' , 2014, 48, 79-94. This paper develops a testing framework for comparing the predictive accuracy of copula-based multivariate density forecasts, focusing on a specific part of the joint distribution. The test is framed in the context of the Kullback-Leibler Information Criterion, but using (out-of-sample) conditional likelihood and censored likelihood in order to focus the evaluation on the region of interest. Monte Carlo simulations document that the resulting test statistics have satisfactory size and power properties in small samples. In an empirical application to daily exchange rate returns we find evidence that the dependence structure varies with the sign and magnitude of returns, such that different parametric copula models achieve superior forecasting performance in different regions of the support. Our analysis highlights the importance of allowing for lower and upper tail dependence for accurate forecasting of common extreme appreciation and depreciation of different currencies.

Suggested Citation

  • 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.
  • Handle: RePEc:tin:wpaper:20130061
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    File URL: https://papers.tinbergen.nl/13061.pdf
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    References listed on IDEAS

    as
    1. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    2. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    3. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2010. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1596-1609, September.
    4. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    7. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    8. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    9. Daniel Berg, 2009. "Copula goodness-of-fit testing: an overview and power comparison," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 675-701.
    10. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
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    12. Wouter Denhaan & Andrew T. Levin, 1996. "VARHAC Covariance Matrix Estimator (GAUSS)," QM&RBC Codes 64, Quantitative Macroeconomics & Real Business Cycles.
    13. James Mitchell & Stephen G. Hall, 2005. "Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ‘Fan’ Charts of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 995-1033, December.
    14. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    15. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    16. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
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    More about this item

    Keywords

    Copula-based density forecast; Kullback-Leibler Information Criterion; out-of-sample forecast evaluation;

    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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