Volatility forecasting with double Markov switching GARCH models

Abstract

This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat-tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first-order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value-at-risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright © 2008 John Wiley & Sons, Ltd.

Markov Switching Integer-Valued Generalized Auto-Regressive Conditional Heteroscedastic Models for Dengue Counts

“…The label switching phenomenon is a fundamental problem for MCMC estimation of the parameters of MS models; see Chen et al (2009). For identification, we use the following restriction to relabel the MCMC output to have higher intensity in state 2.…”

“…The MS auto-regressive model that was introduced by Hamilton (1988) adopts the idea of regime variations in manifold economic and financial time series and continues to gain popularity in time series analysis, e.g. Cai (1994), Hamilton and Susmel (1994), Gray (1996) and Chen et al (2009). Zeger and Qaqish (1988) employed generalized linear models for the conditional distribution of an outcome given its past observations, calling them 'Markov regression models', in which they assumed that the intensity rate is a constant.…”

“…During the last two decades, the literature has widely employed and implemented Bayesian inference for parametric models. For example, see Jung et al (2006) and Lee (2016, 2017) for time series count data and Chen et al (2009) for non-linear financial time series models, who handled the double MS GARCH models in a Bayesian framework. In this study we propose an adapted Markov chain Monte Carlo (MCMC) method for parameter estimation and nowcasting.…”

Bayesian semiparametric Markov switching stochastic volatility model

“…In addition, the authors allowed for all volatility parameters to change across different states as well as the mean equation for the returns, allowing for more flexibility. Chen et al 57 showed that their proposed model is superior to standard approaches in VaR estimation. Define = ( 0 , 1 , , 2 , p, q) as a set of parameters associated with the volatility equation, = {( , 2 ) ( ) } ∞ =1 as a set of parameters associated with the distribution of the error term, and = ( , ) as a complete set of model parameters.…”

Predictive power of Markovian models: Evidence from US recession forecasting

“…The Markov switching model of Hamilton (1989) is widely used for time series in which the autoregressive parameters switch between different time regimes. Studies that implement HMMs include, among others, Hamilton (1990), Lahiri and Moore (1991), Lahiri and Wang (1994), Hamilton and Perez-Quiros (1996), Layton (1996), Gregoir and Lenglart (2000), Ivanova, Lahiri, and Seitz (2000), Marsh (2000), Kontolemis (2001), Koskinen and Öller (2003), Giampieri, Davis, and Crowder (2005), Andersson, Bock, and Frisén (2005), , Banachewicz, Lucas, and Vaart (2008), Chen, So, and Lin (2009), Parikakis and Merika (2009), Pinson and Madsen (2012), Nunes, Natário, and Carvalho (2013), Collet and Leonardi (2014), Dorosiewicz (2016), Hou (2017), Nystrup, Madsen, and Lindström (2017), and Nguyen (2018).…”