Robust Statistical Methods for Detecting Outliers, Anomalies, and Structural Instability in Econometric Data

This chapter develops a robust econometric framework for analyzing macroeconomic and financial data in the presence of outliers, heavy tails, and structural instability. Classical econometric models rely on assumptions of normality and parameter stability that are frequently violated in real economies, especially during crisesand policy changes. The chapter presents the foundations of robustness through contamination models, influence functions, and breakdown points, explaining why traditional estimators such as OLS and the sample mean are highly sensitive to extreme observations. It then introduces tail-risk modeling using Extreme Value Theory (EVT) to capture the fat-tailed behavior. Structural instability is analyzed using break-detection and regime-switching methods An empirical illustration using daily Nifty-50 index returns shows that robust methods detect more anomalies and tail risk than classical techniques. The chapter concludes that robust, tail-aware, and regime-adaptive econometric methods are essential for reliable inference and policy design.