Study and development of hybrid and ensemble forecasting models for air quality index forecasting

In this paper, a viable, robust, and highly accurate additive hybrid model employing autoregressive fractionally integrated moving average (ARFIMA) and support vector machine (SVM) with functionally expanded inputs (Additive-ARFIMA-SVM) is presented for forecasting the air quality index (AQI). Additionally, thirteen additive and multiplicative hybrid models are introduced. Several alternatives in feature engineering employing functional expansion of inputs are incorporated to boost the performance of hybrid models. Furthermore, a gradient whale optimization algorithm with group best leader strategy (GWOA-GBL) based meta-heuristic algorithm is proposed. The missing values are imputed and a variable weight ensemble forecasting model is developed using the proposed GWOA-GBL algorithm. To evaluate the effectiveness of the proposed Additive-ARFIMA-SVM forecasting model with functionally expanded inputs, comparisons are made with sixteen machine learning models, including long short-term memory (LSTM), five statistical models, seventeen hybrid models, and ten variable weight ensemble models. Extensive statistical analyses are carried out on the obtained results considering four accuracy measures that show the statistical supremacy of the proposed Additive-ARFIMA-SVM model and GWOA-GBL algorithm in predicting the AQI time series. The proposed Additive-ARFIMA-SVM model with functionally expanded inputs improves the AQI forecasting performance by 16.34% than autoregressive integrated moving average, 14.47% than ARFIMA, 33.96% than XGBoost, 43.47% than SVM, 49.39% than LSTM, 8.64% than Multiplicative-ARIMA-SVM model considering symmetric mean absolute percentage error. The proposed Additive-ARFIMA-SVM model is so efficient and reliable that it can be applied to forecast other time series like stock price, electricity load, crude oil price, sunspot number, stream flow, flood, drought etc.