Althobaiti Zahrah Fayez
Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia.
Sci Rep. 2025 Jul 16;15(1):25699. doi: 10.1038/s41598-025-11343-w.
Forecasting carbon dioxide (CO₂) emissions has become crucial for attaining environmental sustainability, especially in Bahrain, which uses a lot of fossil fuels. Therefore, there is need for more accurate modeling tools that are suited to Bahrain emission pattern, particularly in light of the increasing environmental pressure and dearth of previous studies. Accordingly, we proposed a hybrid forecasting model that combines Singular Spectrum Analysis (SSA) and the Auto Regressive Integrated Moving Average (ARIMA) method. This hybrid model decomposes the annual CO₂ emissions time series into trend, periodic, and noise components using SSA, then applies ARIMA individually to each component. As a result, the study makes use of World Bank annual CO₂ emission data for three different time periods: 1990-2018, 2000-2018, and 2003-2018. The model performance was evaluated using standard error metrics-Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). To assess whether the observed improvements were statistically significant, the Diebold-Mariano (DM) test was also applied, a widely used method for comparing the predictive accuracy of competing models. In addition, forecast evaluation metrics such as Theil's U-statistic and out-of-sample forecast plots with confidence intervals were also used to strengthen the assessment of the models. Results show that the SSA-ARIMA hybrid model significantly outperforms the conventional ARIMA model. For instance, during the 2014-2018 period, the hybrid model achieved lower MAPE values (1.12%, 0.91%, and 1.40%) compared to ARIMA (2.14%, 1.69%, and 1.41%) across the respective time frames. These results demonstrated the hybrid SSA-ARIMA model's potential as a reliable tool for Bahrain's emissions forecasting.
预测二氧化碳（CO₂）排放对于实现环境可持续性至关重要，特别是在大量使用化石燃料的巴林。因此，需要更适合巴林排放模式的精确建模工具，尤其是考虑到日益增加的环境压力和以往研究的匮乏。相应地，我们提出了一种结合奇异谱分析（SSA）和自回归积分移动平均（ARIMA）方法的混合预测模型。该混合模型使用SSA将年度CO₂排放时间序列分解为趋势、周期和噪声成分，然后分别对每个成分应用ARIMA。结果，该研究使用了世界银行在三个不同时间段的年度CO₂排放数据：1990 - 2018年、2000 - 2018年和2003 - 2018年。使用标准误差指标——平均绝对百分比误差（MAPE）和均方根误差（RMSE）对模型性能进行评估。为了评估观察到的改进是否具有统计学意义，还应用了迪博尔德 - 马里亚诺（DM）检验，这是一种广泛用于比较竞争模型预测准确性的方法。此外，还使用了诸如泰尔U统计量和带有置信区间的样本外预测图等预测评估指标来加强对模型的评估。结果表明，SSA - ARIMA混合模型明显优于传统的ARIMA模型。例如，在2014 - 2018年期间，与ARIMA（分别为2.14%、1.69%和1.41%）相比，混合模型在各个时间范围内实现了更低的MAPE值（1.12%、0.91%和1.40%）。这些结果证明了混合SSA - ARIMA模型作为巴林排放预测可靠工具的潜力。
