Premium
Bayesian tail‐risk forecasting using realized GARCH
Author(s) -
Contino Christian,
Gerlach Richard H.
Publication year - 2017
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2237
Subject(s) - autoregressive conditional heteroskedasticity , econometrics , heteroscedasticity , value at risk , bayesian probability , autoregressive model , statistics , estimator , conditional probability distribution , economics , mathematics , expected shortfall , volatility (finance) , risk management , finance
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.