Modeling volatility using state space models with heavy tailed distributions

This article deals with a non-Gaussian state space model (NGSSM) which is attractive because the likelihood can be analytically computed. The paper focuses on stochastic volatility models in the NGSSM, where the observation equation is modeled with heavy tailed distributions such as Log-gamma, Log-normal and Weibull. Parameter point estimation can be accomplished either using Bayesian or classical procedures and a simulation study shows that both methods lead to satisfactory results. In a real data application, the proposed stochastic volatility models in the NGSSM are compared with the traditional autoregressive conditionally heteroscedastic, its exponential version, and stochastic volatility models using South and North American stock price indexes.