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Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation

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Author Info

  • Lukasz Gatarek

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam)

  • Lennart Hoogerheide

    (VU University Amsterdam)

  • Koen Hooning

    (Delft University of Technology)

  • Herman K. van Dijk

    (Econometric Institute, Erasmus University Rotterdam, and VU University Amsterdam)

Abstract

Accurate prediction of risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) requires precise estimation of the tail of the predictive distribution. Two novel concepts are introduced that offer a specific focus on this part of the predictive density: the censored posterior, a posterior in which the likelihood is replaced by the censored likelihood; and the censored predictive likelihood, which is used for Bayesian Model Averaging. We perform extensive experiments involving simulated and empirical data. Our results show the ability of these new approaches to outperform the standard posterior and traditional Bayesian Model Averaging techniques in applications of Value-at-Risk prediction in GARCH models.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 13-060/III.

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Date of creation: 15 Apr 2013
Date of revision: 06 Mar 2014
Handle: RePEc:dgr:uvatin:20130060

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Web page: http://www.tinbergen.nl

Related research

Keywords: censored likelihood; censored posterior; censored predictive likelihood; Bayesian Model Averaging; Value at Risk; Metropolis-Hastings algorithm.;

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  1. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2012. "Time-varying Combinations of Predictive Densities using Nonlinear Filtering," Tinbergen Institute Discussion Papers 12-118/III, Tinbergen Institute.
  2. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging Using Predictive Measures," CEPR Discussion Papers 5268, C.E.P.R. Discussion Papers.
  3. Lennart Hoogerheide & Richard Kleijn & Francesco Ravazzolo & Herman K. van Dijk & Marno Verbeek, 2009. "Forecast Accuracy and Economic Gains from Bayesian Model Averaging using Time Varying Weights," Tinbergen Institute Discussion Papers 09-061/4, Tinbergen Institute.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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  6. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Post-Print peer-00834423, HAL.
  7. Hoogerheide, Lennart & van Dijk, Herman K., 2010. "Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling," International Journal of Forecasting, Elsevier, vol. 26(2), pages 231-247, April.
  8. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
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  12. repec:taf:jnlbes:v:30:y:2012:i:1:p:1-17 is not listed on IDEAS
  13. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
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