Robustness of the Mean Square Risk in Forecasting of Regression Time Series

Abstract

Abstract Problems of statistical forecasting of time series under distortions of hypothetical models are considered. A classification scheme of the typical distortions of time series is presented and mathematical descriptions of distortions are given. Robustness characteristics for the mean square risk of forecasting (the risk unstability coefficient and the δ-admissible distortion level) are evaluated for the regression time series under outliers and functional distortions. New robust forecasting statistics are constructed. The theoretical results are illustrated by numerical experiments. Keywords: DistortionsForecastingRegressionRiskRobustnessTime seriesMathematics Subject Classification: 62M2062M1062G35 Acknowledgment The author acknowledges the anonymous referees for their valuable comments that helped to improve the article.