Research Reports

Handling Structural Shifts, Outliers and Heavy-Tailed Distributions in State Space Time Series Models

James Durbin & Magdalena Cordero

RR 93/03

ABSTRACT

Time series containing abrupt structural shifts or outliers or both are considered. Techniques are developed for handling these using mixtures of densities, one component of which is a Gaussian density with a large variance. State space models are fitted to the series. The state vectors are estimated by the mode of their posterior density given the observations. The mode is found by Gauss-Newton iteration using Kalman filtering and smoothing. Three approximations to the likelihood function for estimating the hyperparameters are given. The techniques are illustrated by applying them to simulated and real series. The treatment is extended to deal with heavy- tailed densities.