Threshold Stochastic Volatility Models with Heavy Tails: A Bayesian Approach

• Autores: Abanto-Valle, Carlos A., Garrafa-Aragón, Hernán B.
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Pontificia Universidad Católica del Perú
• Repositorio: Revistas - Pontificia Universidad Católica del Perú
• Lenguaje: inglés
• OAI Identifier: oai:ojs.pkp.sfu.ca:article/21103
• Enlace del recurso: http://revistas.pucp.edu.pe/index.php/economia/article/view/21103
• Nivel de acceso: acceso abierto
• Materia: MMarkov chain Monte Carlo; Non linear state space models; Scale mixtures of normal distributions; Stochastic volatility; Threshold; Value-at-Risk; Expected shortfall

This paper extends the threshold stochastic volatility (THSV) model specification proposed in So et 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) and Expected Shortfall (ES) forecasting via a computational Bayesian framework are considered. The MCMC-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), Buenos Aires 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 improve VaR and ES forecasting in comparison with the normal and Student-t models.