Posterior Analysis of State Space Model with Spherical Symmetricity

Abstract

The present work investigates state space model with nonnormal disturbances when the deviation from normality has been observed only with respect to kurtosis and the distribution of disturbances continues to follow a symmetric family of distributions. Spherically symmetric distribution is used to approximate behavior of symmetric nonnormal disturbances for discrete time series. The conditional posterior densities of the involved parameters are derived, which are further utilized in Gibbs sampler scheme for estimating the marginal posterior densities. The state space model with disturbances following multivariate-tdistribution, which is a particular case of spherically symmetric distribution, is discussed.