Noise Robust Hybrid ANFIS-ARIMA Model for Air Pollution Time Series Forecasting

Abstract

This research investigates the performance of a hybrid forecasting approach that integrates the Auto-Regressive Integrated Moving Average (ARIMA) and the Adaptive Neuro-Fuzzy Inference System (ANFIS) models for air pollution time series prediction. The study utilizes daily concentrations of nitrogen dioxide (NO₂) and ozone (O₃) obtained from air quality monitoring stations. Data preprocessing included handling missing values, normalization, and decomposition into trend, seasonal, and residual components, followed by training and testing partition. The individual ANFIS model was first applied to predict pollutant concentrations, showing reliable performance with R² values exceeding 0.90 for both NO₂ and O₃. To enhance accuracy, a hybrid ARIMA–ANFIS model was developed, where ARIMA captured linear patterns and ANFIS modeled the nonlinear residuals. The evaluation was performed under both clean and noisy conditions, with Gaussian noise added at levels of 10%, 20%, and 50% to assess robustness. Results indicated that the hybrid model achieved superior performance on clean data, with an MSE of 0.000338, RMSE of 0.018378, R² of 0.993286, and SMAPE of 4.01%. Although performance slightly declined under noisy conditions, the model maintained strong predictive ability, achieving R² values of 0.983286, 0.954630, and 0.790016 for 10%, 20%, and 50% noise, respectively. These findings confirm that the hybrid ARIMA–ANFIS framework is not only highly accurate but also robust against disturbances, making it a suitable and reliable model for forecasting air pollutant concentrations in real-world scenarios where data uncertainty is common.