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Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

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  • Abanto-Valle, C.A.
  • Bandyopadhyay, D.
  • Lachos, V.H.
  • Enriquez, I.

Abstract

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of-sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model.

Suggested Citation

  • Abanto-Valle, C.A. & Bandyopadhyay, D. & Lachos, V.H. & Enriquez, I., 2010. "Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2883-2898, December.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:2883-2898
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    References listed on IDEAS

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    Cited by:

    1. Sujay Mukhoti & Pritam Ranjan, 2016. "Mean-correction and Higher Order Moments for a Stochastic Volatility Model with Correlated Errors," Papers 1605.02418, arXiv.org.
    2. Ferraz, V.R.S. & Moura, F.A.S., 2012. "Small area estimation using skew normal models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2864-2874.
    3. Auray, Stéphane & Eyquem, Aurélien & Jouneau-Sion, Frédéric, 2014. "Modeling tails of aggregate economic processes in a stochastic growth model," Computational Statistics & Data Analysis, Elsevier, pages 76-94.
    4. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    6. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    7. Sujay Mukhoti & Pritam Ranjan, 2017. "A New Class of Discrete-time Stochastic Volatility Model with Correlated Errors," Papers 1703.06603, arXiv.org.
    8. Mukhoti, Sujay, 2014. "Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness," MPRA Paper 62532, University Library of Munich, Germany.
    9. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, pages 847-859.
    10. Ying Wang & Sai Tsang Boris Choy & Hoi Ying Wong, 2016. "Bayesian Option Pricing Framework with Stochastic Volatility for FX Data," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-12, December.
    11. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2014. "Score driven asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws142618, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Fengkai Yang & Haijing Yuan, 2017. "A Non-iterative Bayesian Sampling Algorithm for Linear Regression Models with Scale Mixtures of Normal Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 579-597, April.
    13. Joshua C.C. Chan, 2015. "Specification tests for time-varying parameter models with stochastic volatility," CAMA Working Papers 2015-42, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    14. Patricia Lengua & Cristian Bayes & Gabriel Rodríguez, 2015. " A Stochastic Volatility Model with GH Skew Student’s t-Distribution: Application to Latin-American Stock Returns," Documentos de Trabajo / Working Papers 2015-405, Departamento de Economía - Pontificia Universidad Católica del Perú.
    15. Roland Langrock & Théo Michelot & Alexander Sohn & Thomas Kneib, 2015. "Semiparametric stochastic volatility modelling using penalized splines," Computational Statistics, Springer, vol. 30(2), pages 517-537, June.
    16. Joshua C.C. Chan & Eric Eisenstat, 2015. "Bayesian model comparison for time-varying parameter VARs with stochastic volatility," CAMA Working Papers 2015-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

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