Bayesian Analysis of Realized Matrix-Exponential GARCH Models
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Bayesian Analysis of Realized Matrix‑Exponential GARCH Models Manabu Asai1 · Michael McAleer2,3,4,5,6 Accepted: 10 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This study develops a new realized matrix-exponential GARCH (MEGARCH) model, which uses the information of returns and realized measure of co-volatility matrix simultaneously. An alternative multivariate asymmetric function to develop news impact curves is also considered. We consider Bayesian Markov chain Monte Carlo estimation to allow non-normal posterior distributions and illustrate the usefulness of the algorithm with numerical simulations for two assets. We compare the realized MEGARCH models with existing multivariate GARCH class models for three US financial assets. The empirical results indicate that the realized MEGARCH models outperform the other models regarding out-of-sample performance. The news impact curves based on the posterior densities provide reasonable results. Keywords Multivariate GARCH · Realized measure · Matrix-exponential · Bayesian Markov chain Monte Carlo method · Asymmetry JEL Classification C11 · C32
* Manabu Asai m‑[email protected] 1
Faculty of Economics, Soka University, Hachioji, Japan
2
Department of Finance, Asia University, Taichung, Taiwan
3
Discipline of Business Analytics, University of Sydney Business School, Sydney, Australia
4
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, The Netherlands
5
Department of Economic Analysis and ICAE, Complutense University of Madrid, Madrid, Spain
6
Institute of Advanced Sciences, Yokohama National University, Yokohama, Japan
13
Vol.:(0123456789)
M. Asai, M. McAleer
1 Introduction Estimation and forecasting time-varying co-volatilities between assets plays an important role in asset pricing, portfolio selections, and risk management. Estimating conditional covariance matrices via the multivariate models of the class of generalized autoregressive conditional heteroskedasticity (GARCH) is a popular approach (e.g., see the survey paper by McAleer 2005). Over the past two decades, realized measures of volatility have received unprecedented attention in the academic literature on modeling and forecasting of stock market returns volatility. In the traditional literature on GARCH models, Engle and Gallo (2006) and Shephard and Sheppard (2010), among others, incorporated realized measures for modeling and forecasting volatility. In addition, Hansen et al. (2012) suggested the realized GARCH framework, which provides a structure for the joint modeling of returns and realized measures of volatility. By extending the aforementioned work, Hansen and Huang (2016) developed the realized exponential GARCH (EGARCH) model, which is an extension of Nelson’s (1991) EGARCH model. The former only use the information contained in the realized co-volatility matrix, and the models in both studies can be improved by considering the difference between realized and unobservable co-volatility
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