Air quality is closely linked to human health and social development, making accurate air quality prediction highly significant. The Air Quality Index (AQI) is inherently a time series. However, most previous studies have overlooked its temporal features and have not thoroughly explored the relationship between pollutant emissions and air quality. To address this issue, this study establishes a historical correlation model for air quality based on a time series model-the Gaussian Hidden Markov Model (GHMM)-using industrial exhaust emissions and historical air quality data. Firstly, a traversal method is used to select the optimal number of hidden states for the GHMM. To optimize the traditional GHMM and reduce error accumulation in the prediction process, the Multi-day Weighted Matching method and the Fixed Training Set Length method are utilized. Both direct and indirect prediction modes are then used to predict the AQI in the Zhangdian District. Experimental results indicate that the improved GHMM with the indirect mode provides higher accuracy and more stable state estimation results (MAE = 13.59, RMSE = 17.59, mean forecasted value = 117.94). Finally, the air quality historical correlation model is integrated with the air quality meteorological correlation model from a previous study, further improving prediction accuracy (MAE = 11.59, RMSE = 14.87, mean forecasted value = 120.88). This study demonstrates that the GHMM's strong ability to analyze temporal features significantly enhances the accuracy and stability of air quality predictions. The integration of the air quality historical correlation model with the air quality meteorological correlation model from a previous study leverages the strengths of each sub-model in handling different feature groups, leading to even more accurate predictions.
