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Out-of-sample Comparison of Copula Specifications in Multivariate Density Forecasts

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Author Info
Cees Diks () (University of Amsterdam)
Valentyn Panchenko () (University of New South Wales)
Dick van Dijk () (Erasmus University Rotterdam)

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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 non-nested. 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.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-105/4.

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Handle: RePEc:dgr:uvatin:20080105

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Related research
Keywords: Copula-based density forecast; semiparametric statistics; out-of-sample forecast evaluation; Kullback-Leibler Information Criterion; empirical copula;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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  1. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July. [Downloadable!] (restricted)
  2. Christian Genest & Jean-François Quessy & Bruno Rémillard, 2006. "Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 33(2), pages 337-366. [Downloadable!] (restricted)
  3. Panchenko, V., 2004. "Goodness-of-fit test for copulas," CeNDEF Working Papers 04-16, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  4. Gianni Amisano & Raffaella Giacomini, 2005. "Comparing Density Forecsts via Weighted Likelihood Ratio Tests," Working Papers ubs0504, University of Brescia, Department of Economics. [Downloadable!]
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  5. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November. [Downloadable!] (restricted)
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  6. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August. [Downloadable!] (restricted)
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  7. 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, 05. [Downloadable!] (restricted)
    Other versions:
  8. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13. [Downloadable!] (restricted)
  9. Andrew J. Patton, 2008. "Copula-Based Models for Financial Time Series," OFRC Working Papers Series 2008fe21, Oxford Financial Research Centre. [Downloadable!]
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