Bayesian Filtering for Markov Switching Stochastic Volatility Model with Heavy Tails

In this paper we study the Markov switching stochastic volatility model with heavy-tails and its applications to capture changes in volatility which is caused by economic forces, market events and so on. Because there are two hidden levels of the latent variable in the model and the state space of the model has a nonlinear structure, it´s difficult to get the analytical solution of the model. In the Bayesian framework we present an efficient auxiliary particle filtering algorithm to filter the hidden states and estimate the parameters. Moreover, we focus on the effect of heavy tails. Simulation demonstrates the performance APF algorithm applied to MSSV-t model compared to the basic MSSV model. Additionally, we apply the model to a real financial time series: the SSE composite index and show its power to distinguish volatility regimes and to improve the estimation precision.