A Spectral Analysis-Driven SARIMAX Framework with Fourier Terms for Monthly Dust Concentration Forecasting
2025
Ommolbanin Bazrafshan | Hossein Zamani | Behnoush Farokhzadeh | Tommaso Caloiero
This study aimed to forecast monthly PM2.5 concentrations in Zabol, one of the world&rsquo:s most dust-prone regions, using four time series models: SARIMA, SARIMAX enhanced with Fourier terms (selected based on spectral peak analysis), TBATS, and a novel hybrid ensemble. Spectral analysis identified a dominant annual cycle (frequency 0.083), which justified the inclusion of two Fourier harmonics in the SARIMAX model. Results demonstrated that the hybrid model, which optimally combined forecasts from the three individual models (with weights &omega:2 = 0.628 for SARIMAX, &omega:3 = 0.263 for TBATS, and &omega:1 = 0.109 for SARIMA), outperformed all others across all evaluation metrics, achieving the lowest AIC (1835.04), BIC (1842.08), RMSE (9.42 &mu:g/m3), and MAE (7.43 &mu:g/m3). It was also the only model exhibiting no significant residual autocorrelation (Ljung&ndash:Box p-value = 0.882). Forecast uncertainty bands were constant across the prediction horizon, with widths of approximately ±:11.39 &mu:g/m3 for the 80% confidence interval and ±:22.25 &mu:g/m3 for the 95% confidence interval, reflecting fixed absolute uncertainty in the multi-step forecasts. The proposed hybrid framework provides a robust foundation for early warning systems and public health management in dust-affected arid regions.
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