Threshold Stochastic Volatility Models with Heavy Tails:A Bayesian Approach

Carlos A. Abanto-Valle and Hernán B. Garrafa-Aragón
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Carlos A. Abanto-Valle: Department of Statistics, Federal University of Rio de Janeiro
Hernán B. Garrafa-Aragón: Escuela de Ingeniería Estadística de la Universidad Nacional de Ingeniería, Lima, Perú

Revista Economía, 2019, vol. 42, issue 83, 32-53

Abstract: This paper extends the threshold stochastic volatility (THSV) model specification proposed in Soet al. (2002) and Chen et al. (2008) by incorporating thick-tails in the mean equation innovation using the scale mixture of normal distributions (SMN). A Bayesian Markov Chain Monte Carlo algorithm is developed to estimate all the parameters and latent variables. Value-at-Risk (VaR) andExpected Shortfall (ES) forecasting via a computational Bayesian framework are considered. TheMCMC-based method exploits a mixture representation of the SMN distributions. The proposed methodology is applied to daily returns of indexes from BM&F BOVESPA (BOVESPA), BuenosAires Stock Exchange (MERVAL), Mexican Stock Exchange (MXX) and the Standar & Poors 500(SP500). Bayesian model selection criteria reveals that there is a significant improvement in model fit for the returns of the data considered here, by using the THSV model with slash distribution over the usual normal and Student-t models. Empirical results show that the skewness can improveVaR and ES forecasting in comparison with the normal and Student-t models.

Keywords: Expected shortfall; Markov chain Monte Carlo; Non linear state space models; Scale mixtures of normal distributions; Stochastic volatility; Threshold; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C11 C15 C51 C52 C58 (search for similar items in EconPapers)
Date: 2019
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