Robust Time Series Analysis through the Forward Search

Abstract

The forward search (FS) is a powerful general method for detecting masked multiple outliers and for determining their effect on models fitted to the data (Atkinson and Riani, 2000). This method was originally introduced for models which assumed independent observations: linear and non linear regression, generalized linear models and multivariate analysis. In this paper we extend the forward search technique to the analysis of time series data. The basic ingredients of the FS are a robust start from an outlier-free subset of observations, a criterion for progressing in the search, which allows the subset to increase by one or more observations at each step, and a set of diagnostic tools that are monitored along the search. The robustness of the FS stems from the very definition of its algorithm, starting from “good” data points and including outliers at the end of the procedure. Computation of high-breakdown estimators is not required, except possibly at the starting stage. Indeed, the application of efficient likelihood or moment based methods at subsequent steps of the FS provides the analyst with more powerful tools than those obtained via traditional high-breakdown estimation.