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Bayesian analysis of stochastic volatility models. (English) Zbl 1082.62103

Shephard, Neil (ed.), Stochastic volatility. Selected readings. Oxford: Oxford University Press (ISBN 0-19-925720-5/pbk; 0-19-925719-1/hbk). Advanced Texts in Econometrics, 247-282 (2005).
Summary: New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty.
We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.
For the entire collection see [Zbl 1076.60005].

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
91B28 Finance etc. (MSC2000)
65C40 Numerical analysis or methods applied to Markov chains
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