Outliers and Switches in Time Series

Abstract

For unobserved components or structural time series models, the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter, such as trend or level changes. The effect of the intervention is measured by the change in the estimates of the individual variances. We examine the effect on these estimated parameters of moving various kinds of intervention along the series. The horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing. Interpretation of the resulting time series plots of diagnostics is aided by simulation envelopes using an approximation to the score statistic. The procedure is illustrated with an example in which the intervention is in the form of a ‘switch’.