Robust Estimation for Time Series Autoregressions

Abstract

This chapter presents some theory and methodology of robust estimation for time series having two distinctive types of outliers. Research on robust estimation in the time series context has lagged behind, and perhaps understandably so in view of the increased difficulties imposed by dependency and the considerable diversity in qualitative features of time series data sets. For time series parameter, estimation problems, efficiency robustness, and min–max robustness are concepts directly applicable. Influence curves for parameter estimates may also be defined without special difficulties. A greater care is needed in defining breakdown points as the detailed nature of the failure mechanism may be quite important. A major problem that remains is that of providing an appropriate and workable definition of qualitative robustness in the time series context. For time series, the desire for a complete probabilistic description of either a nearly-Gaussian process with outliers, or the corresponding asymptotic distribution of parameter estimates, will often dictate that one specify more than a single finite-dimensional distribution of the process. It is only in special circumstances that the asymptotic distribution of the estimate will depend only upon a single univariate distribution or a single multivariate distribution.