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Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors

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  • Xibin Zhang

    ()

  • Maxwell L. King

    ()

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 heavytails. To test for the significance of the Box-Cox transformation parameter, we present the likelihood ratio statistic, in which likelihood functions can be approximated using a particle filter and a Monte Carlo kernel likelihood. When applying the heavy-tailed asymmetric Box-Cox SV model and the proposed sampling algorithm to continuously compounded daily returns of the Australian stock index, we find significant empirical evidence supporting the Box-Cox transformation of the squared volatility against the alternative model involving a logarithmic transformation.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 26/04.

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Length: 28 pages
Date of creation: Nov 2004
Date of revision:
Handle: RePEc:msh:ebswps:2004-26

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Keywords: Leverage effect; Likelihood ratio test; Markov Chain Monte Carlo; Monte Carlo kernel likelihood; Particle filter;

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References

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Citations

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Cited by:
  1. Harvey, A. & Chakravarty, T., 2008. "Beta-t-(E)GARCH," Cambridge Working Papers in Economics 0840, Faculty of Economics, University of Cambridge.
  2. 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.
  3. Xibin Zhang & Maxwell L. King, 2004. "Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors," Monash Econometrics and Business Statistics Working Papers 26/04, Monash University, Department of Econometrics and Business Statistics.
  4. Georgios Tsiotas, 2009. "On the use of non-linear transformations in Stochastic Volatility models," Statistical Methods and Applications, Springer, vol. 18(4), pages 555-583, November.
  5. Weigand, Roland, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," University of Regensburg Working Papers in Business, Economics and Management Information Systems 478, University of Regensburg, Department of Economics.
  6. 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.
  7. María José Rodríguez & Esther Ruiz, 2009. "GARCH models with leverage effect : differences and similarities," Statistics and Econometrics Working Papers ws090302, Universidad Carlos III, Departamento de Estadística y Econometría.
  8. Zhongxian Men & Adam W. Kolkiewicz & Tony S. Wirjanto, 2013. "Bayesian Inference of Asymmetric Stochastic Conditional Duration Models," Working Paper Series 28_13, The Rimini Centre for Economic Analysis.
  9. 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.

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