Robust estimation iin time series: an approximation to the gaussian sum filter

Abstract

This paper proposes a filter which can track the level of a time series robustly and adapt well to step jumps. The filter, called the approximate Gaussian sum filter (AGSF), is derived from the Gaussian sum filter by collapsing the terms in the normal mixtures. Besides producing one-step ahead forecasts robust towards additive and innovation outliers, the filter also estimates the scale parameters in the local level model separately from the variability caused by contamination. Simulation results show that the AGSF produces robust estimates of the hyperparameters regardless of the underlying distributions of the error terms. An example is included to illustrate the robust tracking of the series level by the AGSF as compared with the Kalman filter and an additive outlier filter.