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.

This study investigates the returns and volatility of bull and bear markets as represented by the Tokyo Stock Price Index (TOPIX). Our results show that bull markets are characterized by high returns and low volatility and that the opposite is true for bear markets. Further, this study uncovers a relationship between the duration of bull and bear markets and the point at which the TOPIX has turned from bull to bear and vice versa. Our results indicate that a bull or bear market has a higher probability of continuing as the duration of market's current trend lengthens. If a bull or bear market trend persists for more than nine months, its probability of continuing approaches 1. Conversely, the transition from a rising to a declining market, and vice versa, is more likely to occur when the previous trend has persisted for less than nine months.

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