Time Series Prediction of the AQI in Wuhan City via a Hybrid Prophet–LSTM Model with an Improved PSO Algorithm

The air quality index (AQI) depends on the concentrations of six pollutants (PM2.5, PM10, SO2, NO2, O3, and CO). We propose a hybrid Prophet–LSTM forecasting framework with an improved particle swarm optimization (PSO) algorithm to tune the fusion weight. Prophet captures low–frequency trends and seasonality, while LSTM models residual dynamics; PSO selects weights on a validation subset to avoid test leakage. For the Wuhan PM2.5 test period (1 January 2021 to 3 May 2021), the PSO–enhanced hybrid achieves an MAE = 11.234 and an RMSE = 15.009, corresponding to 35.82%/35.10% reductions in the MAE/RMSE compared with Prophet and 37.69%/40.55% reductions compared with LSTM; it also improves over the unoptimized Prophet–LSTM by 6.70% (MAE) and 4.48% (RMSE). A Diebold–Mariano test indicates a statistically significant improvement over Prophet (p = 0.001), whereas the difference relative to LSTM is not significant at the 0.05 level (p = 0.248). Additional experiments on PM10, SO2, CO, NO2, and O3 show that the proposed framework achieves the lowest or near–lowest errors in most cases.