IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v17y2015i3d10.1007_s11009-013-9389-9.html
   My bibliography  Save this article

Bayesian Estimation of a Skew-Student-t Stochastic Volatility Model

Author

Listed:
  • C. A. Abanto-Valle

    (Federal University of Rio de Janeiro)

  • V. H. Lachos

    (Campinas State University)

  • Dipak K. Dey

    (University of Connecticut)

Abstract

In this paper we present a stochastic volatility (SV) model assuming that the return shock has a skew-Student-t distribution. This allows a parsimonious, flexible treatment of skewness and heavy tails in the conditional distribution of returns. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed and used for parameter estimation and forecasting. The MCMC method exploits a skew-normal mixture representation of the error distribution with a gamma distribution as the mixing distribution. The developed methodology is applied to the NASDAQ daily index returns. Bayesian model selection criteria as well as out-of-sample forecasting in a value-at-risk (VaR) study reveal that the SV model based on skew-Student-t distribution provides significant improvement in model fit as well as prediction to the NASDAQ index data over the usual normal model.

Suggested Citation

  • C. A. Abanto-Valle & V. H. Lachos & Dipak K. Dey, 2015. "Bayesian Estimation of a Skew-Student-t Stochastic Volatility Model," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 721-738, September.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9389-9
    DOI: 10.1007/s11009-013-9389-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-013-9389-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-013-9389-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
    2. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    3. 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.
    4. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    5. Michael McAleer & Bernardo da Veiga, 2008. "Single-index and portfolio models for forecasting value-at-risk thresholds," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 217-235.
    6. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    7. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    8. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
    9. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    10. Tsiotas, Georgios, 2012. "On generalised asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 151-172, January.
    11. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 84-108.
    12. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    13. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    14. Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.
    15. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    16. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    17. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    18. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    19. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    20. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    21. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    22. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    23. Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
    24. Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2006. "Investigating asymmetry in US stock market indexes: evidence from a stochastic volatility model," Applied Financial Economics, Taylor & Francis Journals, vol. 16(6), pages 479-490.
    25. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. P. de Zea Bermudez & J. Miguel Marín & Helena Veiga, 2020. "Data cloning estimation for asymmetric stochastic volatility models," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 1057-1074, November.
    2. Iseringhausen, Martin, 2020. "The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 275-292.
    3. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Lengua Lafosse, Patricia & Rodríguez, Gabriel, 2018. "An empirical application of a stochastic volatility model with GH skew Student's t-distribution to the volatility of Latin-American stock returns," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 155-173.
    5. Makoto Nakakita & Teruo Nakatsuma, 2021. "Bayesian Analysis of Intraday Stochastic Volatility Models of High-Frequency Stock Returns with Skew Heavy-Tailed Errors," JRFM, MDPI, vol. 14(4), pages 1-29, March.
    6. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lengua Lafosse, Patricia & Rodríguez, Gabriel, 2018. "An empirical application of a stochastic volatility model with GH skew Student's t-distribution to the volatility of Latin-American stock returns," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 155-173.
    2. Iseringhausen, Martin, 2020. "The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 275-292.
    3. Tsiotas, Georgios, 2012. "On generalised asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 151-172, January.
    4. Patricia Lengua Lafosse & 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.
    5. 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.
    6. Vijverberg, Chu-Ping C. & Vijverberg, Wim P.M. & Taşpınar, Süleyman, 2016. "Linking Tukey’s legacy to financial risk measurement," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 595-615.
    7. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    8. repec:cte:wsrepe:ws131110 is not listed on IDEAS
    9. Carlos A. Abanto‐Valle & Roland Langrock & Ming‐Hui Chen & Michel V. Cardoso, 2017. "Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(4), pages 394-408, August.
    10. Chen, Liyuan & Zerilli, Paola & Baum, Christopher F., 2019. "Leverage effects and stochastic volatility in spot oil returns: A Bayesian approach with VaR and CVaR applications," Energy Economics, Elsevier, vol. 79(C), pages 111-129.
    11. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    12. Alexios Ghalanos & Eduardo Rossi & Giovanni Urga, 2015. "Independent Factor Autoregressive Conditional Density Model," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 594-616, May.
    13. Shi Bo & Minheng Xiao, 2022. "Data-Driven Risk Measurement by SV-GARCH-EVT Model," Papers 2201.09434, arXiv.org, revised Jul 2024.
    14. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    15. Matteo Grigoletto & Francesco Lisi, 2011. "Practical implications of higher moments in risk management," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 487-506, November.
    16. Diks, Cees & Fang, Hao, 2020. "Comparing density forecasts in a risk management context," International Journal of Forecasting, Elsevier, vol. 36(2), pages 531-551.
    17. repec:cte:wsrepe:ws142618 is not listed on IDEAS
    18. Carlos A. Abanto-Valle & Gabriel Rodríguez & Luis M. Castro Cepero & Hernán B. Garrafa-Aragón, 2024. "Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1775-1801, September.
    19. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
    20. Carlos A. Abanto-Valle & Hernán B. Garrafa-Aragón, 2019. "Threshold Stochastic Volatility Models with Heavy Tails:A Bayesian Approach," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, vol. 42(83), pages 32-53.
    21. Mukhoti, Sujay, 2014. "Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness," MPRA Paper 62532, University Library of Munich, Germany.
    22. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9389-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.