Bayesian Realized-GARCH Models for Financial Tail Risk Forecasting Incorporating Two-sided Weibull Distribution

TL;DR

This paper extends realized GARCH models by incorporating a two-sided Weibull distribution and employs sub-sampling techniques, demonstrating improved tail risk forecasting accuracy in financial markets during a six-year period including the financial crisis.

Contribution

The paper introduces a Bayesian realized GARCH model with a two-sided Weibull distribution and sub-sampling methods, enhancing tail risk forecasting in financial time series.

Findings

Realized GARCH models with two-sided Weibull outperform traditional models.

Sub-sampling improves estimation accuracy by reducing micro-structure noise.

Models perform well during the global financial crisis period.

Abstract

The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed in the realized GARCH framework. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is developed and employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH, GARCH with two-sided Weibull distribution and realized GARCH models, tail risk forecasting results across 7 market index return series and 2 individual assets clearly favor the realized GARCH models incorporating two-sided Weibull distribution, especially models employing the sub-sampled realized variance and sub-sampled realized range, over a six year period that includes the global financial crisis.