Sequential Gibbs Particle Filter Algorithm with an Application to Stochastic Volatility and Jumps Estimation

Abstract

The aim of this paper is to propose and test a novel PF method called Sequential Gibbs Particle Filter allowing to estimate complex latent state variable models with unknown parameters. The framework is applied to a stochastic volatility model with independent jumps in returns and volatility. The implementation is based on a novel design of adapted proposal densities making convergence of the model relatively efficient as verified on a testing dataset. The empirical study applies the algorithm to estimate stochastic volatility with jumps in returns and volatility model based on the Prague stock exchange returns. The results indicate surprisingly weak jump in returns components and a relatively strong jump in volatility components with jumps in volatility appearing at the beginning of crisis periods.