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Bayesian tail‐risk forecasting using realized GARCH

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  • Christian Contino
  • Richard H. Gerlach

Abstract

A realized generalized autoregressive conditional heteroskedastic (GARCH) model is developed within a Bayesian framework for the purpose of forecasting value at risk and conditional value at risk. Student‐t and skewed‐t return distributions are combined with Gaussian and student‐t distributions in the measurement equation to forecast tail risk in eight international equity index markets over a 4‐year period. Three realized measures are considered within this framework. A Bayesian estimator is developed that compares favourably, in simulations, with maximum likelihood, both in estimation and forecasting. The realized GARCH models show a marked improvement compared with ordinary GARCH for both value‐at‐risk and conditional value‐at‐risk forecasting. This improvement is consistent across a variety of data and choice of distributions. Realized GARCH models incorporating a skewed student‐t distribution for returns are favoured overall, with the choice of measurement equation error distribution and realized measure being of lesser importance. Copyright © 2017 John Wiley & Sons, Ltd.

Suggested Citation

  • Christian Contino & Richard H. Gerlach, 2017. "Bayesian tail‐risk forecasting using realized GARCH," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 213-236, March.
    • Handle: RePEc:wly:apsmbi:v:33:y:2017:i:2:p:213-236
    DOI: 10.1002/asmb.2237
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    Cited by:

    1. Chao Wang & Richard Gerlach, 2021. "A Bayesian realized threshold measurement GARCH framework for financial tail risk forecasting," Papers 2106.00288, arXiv.org, revised Oct 2022.
    2. Xing, Dun-Zhong & Li, Hai-Feng & Li, Jiang-Cheng & Long, Chao, 2021. "Forecasting price of financial market crash via a new nonlinear potential GARCH model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    3. Xie, Haibin & Yu, Chengtan, 2020. "Realized GARCH models: Simpler is better," Finance Research Letters, Elsevier, vol. 33(C).
    4. Naimoli, Antonio & Gerlach, Richard & Storti, Giuseppe, 2022. "Improving the accuracy of tail risk forecasting models by combining several realized volatility estimators," Economic Modelling, Elsevier, vol. 107(C).

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