Bayesian tail‐risk forecasting using realized GARCH

Christian Contino and Richard H. Gerlach

Applied Stochastic Models in Business and Industry, 2017, vol. 33, issue 2, 213-236

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.

Date: 2017
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https://doi.org/10.1002/asmb.2237

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:33:y:2017:i:2:p:213-236

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