<p>Reliable air quality forecasting is often constrained by the complex coupling of high-dimensional spatial dependencies and the inherent stochasticity of atmospheric processes. Traditional statistical models frequently struggle with high-dimensional state spaces, whereas deep learning architectures are prone to phase lags and overfitting to local noise. To address these challenges, this study proposes ResLSTM-SAR, a novel residual-driven hybrid framework designed to integrate the strengths of machine learning and classical stochastic modeling for more accurate pollutant concentration forecasting. The proposed method follows a predict-and-correct mechanism. First, a Long Short-Term Memory (LSTM) network is employed to extract the dominant nonlinear features from multivariate time series. Then, a Seasonal Autoregressive Integrated Moving Average (SARIMA) module—refined through ADF stationarity testing and ACF/PACF diagnostics—is introduced to explicitly model and correct the remaining linear autocorrelation structure and diurnal periodicity in the prediction residuals. Systematic experiments involving seven criteria pollutants across 11 monitoring stations in Hangzhou demonstrate that ResLSTM-SAR significantly outperforms multiple benchmark models, including LSTM-Transformer and LSTM-DenseNet. On average, the proposed framework reduces RMSE by 46.32% and MAE by 50.60%, while improving R² by 28.17%. Furthermore, validation on unseen datasets from Beijing and Zhengzhou confirms the robustness of the model across heterogeneous climatic regions without the need for site-specific recalibration. These results suggest that ResLSTM-SAR effectively captures shared physicochemical evolutionary patterns across heterogeneous climatic regions, offering a robust and transferable computational tool for environmental risk assessment and policy intervention.</p>