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 by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non‐Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions 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 functions. The choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally efficient. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.