Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives

The analysis of non-Gaussian time series using state space models is consid ered from both classical and Bayesian perspectives. The treatment in both c ases is based on simulation using importance sampling and antithetic variab les; Markov chain Monte Carlo methods are not employed, Non-Gaussian distur bances for the state equation as well as for the observation equation are c onsidered. Methods for estimating conditional and posterior means of functi ons of the state vector given the observations, and the mean-square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution function s. Choice of importance sampling densities and antithetic variables is disc ussed. The techniques work well in practice and are computationally efficie nt. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.