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Markov chain Monte Carlo methods for stochastic volatility models. (English) Zbl 1099.62539
Summary: This paper is concerned with simulation-based inference in generalized models of stochastic volatility defined by heavy-tailed Student-t distributions (with unknown degrees of freedom) and exogenous variables in the observation and volatility equations and a jump component in the observation equation. By building on the work of {\it S. Kim, N. Shephard} and {\it S. Chib} [Rev. Econ. Stud. 65, No. 3, 361--393 (1998; Zbl 0910.90067)], we develop efficient Markov chain Monte Carlo algorithms for estimating these models. The paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods. Computation of the marginal likelihood by the method of {\it S. Chib} [J. Am. Stat. Assoc. 90, No. 432, 1313--1321 (1995; Zbl 0868.62027)] is also considered. The methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the S&P 500 index where several stochastic volatility models are formally compared under different priors on the parameters.

MSC:
62P05Applications of statistics to actuarial sciences and financial mathematics
65C40Computational Markov chains (numerical analysis)
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References:
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