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

Author

Listed:
  • 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.

Suggested Citation

  • Lukasz Gatarek & Lennart Hoogerheide & Koen Hooning & Herman K. van Dijk, 2013. "Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation," Tinbergen Institute Discussion Papers 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
  • Handle: RePEc:tin:wpaper:20130060
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    References listed on IDEAS

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    More about this item

    Keywords

    censored likelihood; censored posterior; censored predictive likelihood; Bayesian Model Averaging; Value at Risk; Metropolis-Hastings algorithm.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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