Bayesian Analysis of a Markov Switching Stochastic Volatility Model

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.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

“…For instance, in this paper the estimated volatility of financial asset return changes does not accommodate sudden structural breaks. Recently, the SV model with jumps (Barndorff-Nielsen and Shephard, 2001; Chib et al, 2002) and the regime switching models (So et al, 1998; Shibata and Watanabe, 2005; Abanto-Valle et al, 2009) have received considerable attention. The volatility of daily stock index returns has been estimated with SV models but usually results have relied on extensive pre-modeling of these series, thus avoiding the problem of simultaneous estimation of the mean and variance.…”

Bayesian modeling of financial returns: A relationship between volatility and trading volume

“…According to the CD values, the null hypothesis that the sequence of 50 000 draws is stationary is accepted at the 5% level for all the parameters in all the models considered here. [13,24,35]. On the other hand, the posterior mean and the 95% interval of 2 are 0.1456 and (0.1010, 0.2080), which are higher than the 0.0588 and (0.0353, 0.0940) in the SV model and the 0.0641 and (0.0388, 0.0971) in the SVt model.…”

“…Multi-move samplers have been used to update the log-volatilities. For example, So et al [13] use the mixture sampler Gibbs sampling [18,24] the block sampler Gibbs sampling [25,26].…”

Bayesian semiparametric Markov switching stochastic volatility model

“…The volatility of the S&P500 index is in the high regime during the years 1999-2001 (could be attributed to the dot-com bubble) and 2008-2010 (financial crisis). Table 3 presents the estimated parameter means and [32][33][34][35] among others). Table 4 presents the LPS, LPTS , and LPBF for the S&P500 data.…”

“…Kalimipalli and Susmel 34 considered two-factor SV model with regime switching and found that the estimated high volatility persistence is reduced when the regimes are incorporated in the model. Shibata and Watanabe 35 also found that the persistence parameter estimates drop as compared to those of the standard SV models. Moreover, for their data, the MSSV model performs better than the benchmark SV models.…”