An adaptive autoregressive integration model for multi-variate time series analysis of extreme climate events.

Summer droughts are becoming increasingly severe under climate change, posing significant threats to global food security and ecosystem stability. While multivariate time series (MTS) analysis has emerged as a powerful tool for environmental modeling, it suffers from two limitations: (1) failure to account for temporal volatility patterns, and (2) difficulty in capturing non-stationary relationships among meteorological variables. Therefore, we introduce an innovative goal-oriented adaptive autoregressive integration system, i.e., Multi-Variate Time Series Former (MVformer) by integrating three modules: (1) an Adaptive Sampling Autoregressive Prediction (ASAP) module that dynamically balances teacher forcing and autoregression; (2) a volatility neural network capturing nonlinear temporal dependencies; and (3) extreme clustering for automated pattern discovery. MVformer first processes MTS through ASAP using causal attention and sliding windows for enhanced long-term forecasting, then fuses predictions with historical data into high-dimensional features for density-based extremal clustering to detect droughts. We validate MVformer based on meteorological data from 2,415 Chinese monitoring stations. Experiments show MVformer achieves optimal prediction accuracy (MSE: 0.617, MAE: 0.402, MAPE: 21.945%) and clustering quality (Inertia: 0.004, Silhouette Score: 0.424, Calinski-Harabasz: 767.442, Dunn index: 0.072). In summary, this study provides a robust predictive model for climate monitoring, drought early warning, and agricultural risk management.