The current review addresses the integration of outlier detection, time series forecasting, and machine learning algorithms into the area of Early Warning Systems in the Artificial Intelligence (AI) based economic crisis prediction in the natural and environmental shock. The climate-related losses may have outliers in environmental economics because this type of loss is hard to forecast and appears to be a sudden energy surge or an unexpected pollution spike. The classical methods of statistics analyzed include Mahalanobis Distance and Minimum Covariance Determinant, while advanced methods include Local Outlier Factor, Isolation Forest, and Robust PCA, and their application in working with high-dimensional data. It also stresses machine learning algorithms such as Long Short-Term Memory networks and Random Forests in time series prediction. It puts an emphasis on scalability, robustness, and interpretability, and it shows how artificial intelligence-powered systems can contribute to preparedness, resilience, and policy reaction to risks.