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Box-Cox stochastic volatility models with heavy-tails and correlated errors

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  • Zhang, Xibin
  • King, Maxwell L.

Abstract

This paper presents a Markov chain Monte Carlo (MCMC) algorithm to estimate parameters and latent stochastic processes in the asymmetric stochastic volatility (SV) model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution and the marginal density of asset returns has heavy-tails. We employed the Bayes factor and the Bayesian information criterion (BIC) to examine whether the Box-Cox transformation of squared volatility is favored against the log-transformation. When applying the heavy-tailed asymmetric Box-Cox transformed SV model, three competing SV models and the t-GARCH(1,1) model to continuously compounded daily returns of the Australian stock index, we find that the Box-Cox transformation of squared volatility is strongly favored by Bayes factors and BIC against the log-transformation. While both criteria strongly favor the t-GARCH(1,1) model against the heavy-tailed asymmetric Box-Cox transformed SV model and the other three competing SV models, we find that SV models fit the data better than the t-GARCH(1,1) model based on a measure of closeness between the distribution of the fitted residuals and the distribution of the model disturbance. When our model and its competing models are applied to daily returns of another five stock indices, we find that in terms of SV models, the Box-Cox transformation of squared volatility is strongly favored against the log-transformation for the five data sets.

Suggested Citation

  • Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
  • Handle: RePEc:eee:empfin:v:15:y:2008:i:3:p:549-566
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    Cited by:

    1. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    2. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    3. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    4. Gong, Xu & Wen, Fenghua & Xia, X.H. & Huang, Jianbai & Pan, Bin, 2017. "Investigating the risk-return trade-off for crude oil futures using high-frequency data," Applied Energy, Elsevier, vol. 196(C), pages 152-161.
    5. Harvey, A. & Chakravarty, T., 2008. "Beta-t-(E)GARCH," Cambridge Working Papers in Economics 0840, Faculty of Economics, University of Cambridge.
    6. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    7. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    8. Zhongxian Men & Adam W. Kolkiewicz & Tony S. Wirjanto, 2019. "Threshold Stochastic Conditional Duration Model for Financial Transaction Data," JRFM, MDPI, vol. 12(2), pages 1-21, May.
    9. María José Rodríguez & Esther Ruiz, 2012. "Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(4), pages 637-668, September.
    10. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2021. "Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects," JRFM, MDPI, vol. 14(5), pages 1-28, May.
    11. Georgios Tsiotas, 2009. "On the use of non-linear transformations in Stochastic Volatility models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 555-583, November.
    12. Rodríguez, Mª José & Ruiz Ortega, Esther, 2009. "GARCH models with leverage effect : differences and similarities," DES - Working Papers. Statistics and Econometrics. WS ws090302, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    14. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    15. Zhongxian Men & Adam W. Kolkiewicz & Tony S. Wirjanto, 2013. "Bayesian Inference of Asymmetric Stochastic Conditional Duration Models," Working Paper series 28_13, Rimini Centre for Economic Analysis.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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