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Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes

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Author Info
Gareth O. Roberts
Omiros Papaspiliopoulos
Petros Dellaportas
Abstract

We develop Markov chain Monte Carlo methodology for Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. The approach introduced involves expressing the unobserved stochastic volatility process in terms of a suitable marked Poisson process. We introduce two specific classes of Metropolis-Hastings algorithms which correspond to different ways of jointly parameterizing the marked point process and the model parameters. The performance of the methods is investigated for different types of simulated data. The approach is extended to consider the case where the volatility process is expressed as a superposition of Ornstein-Uhlenbeck processes. We apply our methodology to the US dollar-Deutschmark exchange rate. Copyright 2004 Royal Statistical Society.

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1369-7412.2004.05139.x
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Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

Volume (Year): 66 (2004)
Issue (Month): 2 ()
Pages: 369-393
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Handle: RePEc:bla:jorssb:v:66:y:2004:i:2:p:369-393

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  1. Chris M Strickland & Gael Martin & Catherine S Forbes, 2006. "Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models," Monash Econometrics and Business Statistics Working Papers 22/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  2. Griffin, Jim & Steel, Mark F.J., 2008. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," MPRA Paper 11071, University Library of Munich, Germany. [Downloadable!]
  3. Lancelot F. James, 2005. "Analysis of a Class of Likelihood Based Continuous Time Stochastic Volatility Models including Ornstein-Uhlenbeck Models in Financial Economics," Quantitative Finance Papers math/0503055, arXiv.org, revised Aug 2005. [Downloadable!]
  4. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008. [Downloadable!]
  5. Sylvia Frühwirth-Schnatter & Leopold Sögner, 2009. "Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma law," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(1), pages 159-179, March. [Downloadable!] (restricted)
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