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Bayesian inference for non‐Gaussian Ornstein–Uhlenbeck stochastic volatility processes
Author(s) -
Roberts Gareth O.,
Papaspiliopoulos Omiros,
Dellaportas Petros
Publication year - 2004
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1369-7412.2004.05139.x
Subject(s) - stochastic volatility , ornstein–uhlenbeck process , markov chain monte carlo , bayesian inference , econometrics , bayesian probability , inference , volatility (finance) , point process , gaussian process , mathematics , computer science , statistical physics , gaussian , stochastic process , artificial intelligence , statistics , physics , quantum mechanics
Summary. 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.