Outliers, structural shifts and heavy-tailed distributions in state space time series models

Abstract

In this work a general method is developed for handling outliers, structural shifts and heavy-tailed distributions in linear state space time series models. The basic tool we use for dealing with outliers and structural shifts is to model observation or state error densities by a mixture of densities, one component of which is a Gaussian density with a large variance. The other component can be a Gaussian density, a non-Gaussian density such as Student’s t or it can itself be a Gaussian mixture. The underlying idea is to estimate the state vector by its posterior mode using linearisation, iteration and the Kalman filter and smoother.