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Estimation of Hyperbolic Diffusion Using MCMC Method

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  • Y.K. Tse
  • Xibin Zhang

    ()

  • Jun Yu

Abstract

In this paper we propose a Bayesian method for estimating hyperbolic diffusion models. The approach is based on the Markov Chain Monte Carlo (MCMC) method after discretization via the Milstein scheme. Our simulation study shows that the hyperbolic diffusion exhibits many of the stylized facts about asset returns documented in the financial econometrics literature, such as slowly declining autocorrelation function of absolute terms. We demonstrate that the MCMC method provides a useful tool to analyze hyperbolic diffusions. In particular, quantities of posterior distributions obtained from MCMC outputs can be used for statistical inferences.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2002/wp18-02.pdf
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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 18/02.

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Length: 21 pages
Date of creation: Sep 2002
Date of revision:
Handle: RePEc:msh:ebswps:2002-18

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Related research

Keywords: Markov Chain Monte Carlo; Hyperbolic diffusion; Milstein approximation; ARCH; Long Memory.;

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References

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  1. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  2. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
  3. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
  4. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  6. Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-98, April.
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Citations

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Cited by:
  1. Rob L. Hyndman & Xibin Zhang & Maxwell L. King,, 2004. "Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC," Econometric Society 2004 Australasian Meetings 120, Econometric Society.
  2. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
  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. Peter C.B.Phillips & Jun Yu, . "Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance," Working Papers CoFie-08-2009, Sim Kee Boon Institute for Financial Economics.
  5. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2013. "Bayesian bandwidth selection for a nonparametric regession model with mixed types of regressors," Monash Econometrics and Business Statistics Working Papers 13/13, Monash University, Department of Econometrics and Business Statistics.
  6. Denitsa Stefanova, 2012. "Stock Market Asymmetries: A Copula Diffusion," Tinbergen Institute Discussion Papers 12-125/IV/DSF45, Tinbergen Institute.
  7. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2013. "A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 20/13, Monash University, Department of Econometrics and Business Statistics.
  8. Denitsa Stefanova, 2012. "Stock Market Asymmetries: A Copula Diffusion," Tinbergen Institute Discussion Papers 12-125/IV/DSF45, Tinbergen Institute.
  9. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2012. "Bayesian Approaches to Non-parametric Estimation of Densities on the Unit Interval," Monash Econometrics and Business Statistics Working Papers 3/12, Monash University, Department of Econometrics and Business Statistics.
  10. Xibin Zhang & Robert D. Brooks & Maxwell L. King, 2007. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Monash Econometrics and Business Statistics Working Papers 11/07, Monash University, Department of Econometrics and Business Statistics.
  11. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2011. "Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 10/11, Monash University, Department of Econometrics and Business Statistics.

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