Statistically Robust Time Series Analysis under Data Contamination: A Unified Framework for Modeling, Monitoring, and Forecasting

Classical time series models depend strongly on strict distributional assumptions, particularly normality and the absence of outliers. In practice, many real-world time series datasets violate these assumptions due to measurement errors, extreme observations, or structural changes over time. Such departures may significantly reduce the accuracy of parameter estimation and weaken forecasting performance. Robust time series analysis offers statistically stable techniques that limit the influence of outliers and heavy-tailed disturbances while maintaining efficiency when the underlying assumptions are approximately satisfied. This paper provides a comprehensive review of robust approaches in time series modeling, estimation, change detection, and forecasting. Robust extensions of ARMA and ARIMA models, M-estimation procedures, heavy-tailed error distributions, and robust change-point detection methods are presented, supported by mathematical formulations and practical interpretations.