Robust Methods for Time Series Analysis under Outliers and Heavy-Tailed Distributions

Classical time series models rely heavily on distributional assumptions such as normality and the absence of outliers. However, real-world time series data frequently exhibit deviations from these assumptions due to measurement errors, extreme events, or structural changes. These deviations can severely deteriorate estimation accuracy and forecasting performance. Robust time series analysis provides statistically stable methods that reduce sensitivity to outliers and heavy-tailed noise while preserving efficiency under ideal conditions. This paper presents a comprehensive overview of robust methodologies for time series modeling, estimation, change detection, and forecasting. Robust extensions of ARMA/ARIMA models, M-estimation techniques, heavy-tailed error modeling, and robust change-point detection methods are discussed with mathematical formulations and practical insights.