Optimality and robustness in statistical forecasting

Abstract

The statistical forecasting (prediction) problem of time series is considered for the typical in practice situation where the underlying hypothetical data model is distorted. We present a review of our solutions for the following topical problems of optimality and robustness in statistical forecasting: mathematical description of distortions for typical hypothetical models of time series; quantitative evaluation of the risk-robustness (sensitivity analysis) under distortions for traditional forecasting statistics (that are optimal under hypothetical models); evaluation of critical distortion levels; construction of new robust forecasting statistics.