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

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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.

Keywords: Data augmentation; Lévy processes; Marked point processes; Markov chain Monte Carlo methods; Non-centred parameterizations; Stochastic volatility

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1369-7412.2004.05139.x

Affiliations: 1: Lancaster University, UK. 2: Athens University of Economics and Business, Greece

Publication date: April 1, 2004

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