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

  • Xibin Zhang

    ()

  • Maxwell L. King

    ()

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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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp26-04.pdf
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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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  1. John Y. Campbell & Albert S. Kyle, 1988. "Smart Money, Noise Trading and Stock Price Behavior," NBER Technical Working Papers 0071, National Bureau of Economic Research, Inc.
  2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  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.
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  8. Tim Bollerslev & Hao Zhou, 2003. "Volatility puzzles: a unified framework for gauging return-volatility regressions," Finance and Economics Discussion Series 2003-40, Board of Governors of the Federal Reserve System (U.S.).
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  24. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
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  27. Y.K. Tse & Xibin Zhang & Jun Yu, 2002. "Estimation of Hyperbolic Diffusion Using MCMC Method," Monash Econometrics and Business Statistics Working Papers 18/02, Monash University, Department of Econometrics and Business Statistics.
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