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Block sampler and posterior mode estimation for asymmetric stochastic volatility models

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  • Omori, Yasuhiro
  • Watanabe, Toshiaki

Abstract

A new efficient simulation smoother and disturbance smoother are introduced for asymmetric stochastic volatility models where there exists a correlation between today's return and tomorrow's volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state-space model. The performance of our method is illustrated using two examples: (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 6 (February)
Pages: 2892-2910

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Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:2892-2910

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  8. Yasuhiro Omori & Toshiaki Watanabe, 2007. "Block Sampler and Posterior Mode Estimation for A Nonlinear and Non-Gaussian State-space Model with Correlated Errors," CIRJE F-Series CIRJE-F-508, CIRJE, Faculty of Economics, University of Tokyo.
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  16. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
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