*J. Japan Statist. Soc.,* Vol. 35 (No. 2), pp. 205-219, 2005

## Bayesian Analysis of a Markov Switching Stochastic Volatility Model

Mai Shibata and Toshiaki Watanabe

**Abstract. **
This article analyzes a Markov switching stochastic volatility (MSSV) model to accommodate the shift in the mean of log-volatility. Since it is difficult to estimate the parameters in this model based on the maximum likelihood method, a Bayesian Markov-chain Monte Carlo (MCMC) approach is adopted. A particle filter for the MSSV model, which is used for model comparison and diagnostics, is constructed. The estimation result, based on weekly returns of the TOPIX, confirms the finding by previous researchers that the estimate of the persistence parameter drops and the estimate of the error variance rises in the volatility equation of the MSSV model compared to those of the standard SV model. The model comparison provides evidence that the MSSV model is favored over the standard SV model. It is also found that the MSSV model passes the diagnostic tests based on the statistics obtained from the particle filter while the SV model does not.

*Key words and phrases*:
Marginal likelihood, Markov-chain Monte Carlo, Markov switching, particle filter, stochastic volatility, TOPIX.

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