Robustness in Statistical Forecasting

Abstract

Statistical forecasting procedures are used to solve many applied problems in engineering, economics, finance, medicine, environmental studies, etc. For the majority of the developed statistical forecasting procedures, optimality (or asymptotic optimality as observation time increases) is proved w.r.t. the mean square forecast risk under the assumptions of an underlying hypothetical model. In practice, however, the observed data usually deviates from hypothetical models: random observation errors may be non-Gaussian, correlated, or inhomogeneous; the data may be contaminated by outliers, level shifts, or missing values; trend, regression, and autoregression functions do not necessarily belong to the declared parametric families, etc. Unfortunately, the forecasting procedures which have been proved to be optimal under the hypothetical model often become unstable under even small model distortions, resulting in forecast risks or mean square errors which are significantly higher than the theoretical values obtained in the absence of distortion. This necessitates the development of robust statistical algorithms, which are designed to retain most of their properties under small deviations from model assumptions.