Sequential Bayesian analysis for semiparametric stochastic volatility model with applications

The stochastic volatility (SV) model is widely used to study time-varying volatility. However, the linearity assumption for transition equation in basic SV model is restrictive. To allow for nonlinearity, we proposed a semiparametric SV model that specifies a nonparametric transition equation for log-volatility using natural cubic splines. To estimate the semiparametric SV model, we used the sequential Monte Carlo algorithm and particle Markov chain Monte Carlo methods, which are shown to be able to provide effective estimates of the model in simulation studies. The empirical applications to Bitcoin and convertible bond return data indicate that the transition equations of their log-volatility are highly nonlinear. Taking nonlinearity into account, the semi -parametric SV model can improve the likelihood of the basic SV model both in-sample and out-of-sample. Furthermore, the semiparametric SV model produces more flexible estimated volatility and can better filter out volatility clustering characteristics in original return data.