Monthly PM2.5 Forecasting with Temporally Constrained Rolling Decomposition and DenseMamba

The reliable monthly forecasting of fine particulate matter (PM2.5) requires artificial intelligence (AI) models that are accurate, temporally valid, and transparent. We develop a history-only rolling-decomposition framework with lightweight Mamba-inspired selective state-space backbones for 475 city-level administrative units in China. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and three alternative decomposition strategies use only the PM2.5 data available before each decomposition cutoff, thereby avoiding future-information leakage and yielding inspectable multi-scale predictors. In the primary seven-model benchmark, CEEMDAN-DenseMamba achieved the lowest mean root mean squared error and mean absolute error (6.931 and 4.833 μg m−3, respectively). Equal-optimization reruns, paired moving-block bootstrap intervals, component-count sensitivity, city-wise diagnostics, and a parameter-matched gated recurrent unit baseline were then used to examine performance attribution. Under common optimization, the dense-connection contrasts showed paired error reductions with confidence intervals below zero, whereas the incremental CEEMDAN effect within a fixed backbone was smaller and its paired confidence intervals crossed zero. The recurrent baseline remained competitive. These findings support transparent, temporally valid multi-scale forecasting while limiting inference to future-month prediction for the known cities and the present experimental setting.