基于改进SARIMA模型的比较分析与实证研究

Comparative Analysis and Empirical Research Based on Improved SARIMA Model

摘要: 为提升季节性周期波动数据的预测精度，本研究提出融合一阶滞后滤波的改进SARIMA模型，通过一阶滞后滤波算法过滤部分极端值对模型参数的影响，增强了数据平稳性。同时，本论文通过分析山东省2015~2019年铁路月度客流量数据，对比研究了经典SARIMA(3,1,0) × (1,1,0)₁₂模型与改进SARIMA(0,1,1) × (1,1,0)₁₂模型的性能及预测效果。最终实证表明，改进模型的残差通过白噪声检验(LB检验P > 0.05)，各参数都t检验显著(P < 0.001)；同时在测试集(2019年8~12月)预测准确度与预测稳健性上有明显提高；AIC (660.44)与BIC (665.65)显著优化。该方法在一定程度上提升了传统SARIMA模型的预测稳健性，为高噪声交通数据预测提供一种有效的解决方案。

Abstract: To improve the prediction accuracy of seasonal cycle fluctuation data, this study proposes an improved SARIMA model that integrates first-order lag filtering. The first-order lag filtering algorithm is used to filter out the influence of some extreme values on the model parameters, enhancing the stationarity of the data. At the same time, this paper analyzes the monthly passenger flow data of railways in Shandong Province from 2015 to 2019, and compares the performance and prediction effects of the classic SARIMA(3,1,0) × (1,1,0)₁₂ model and the improved SARIMA(0,1,1) × (1,1,0)₁₂ model. The final empirical results showed that the residuals of the improved model passed the white noise test (LB test P > 0.05), and all parameters were t-test significant (P < 0.001); At the same time, there was a significant improvement in both prediction accuracy and robustness in the test set (August~December 2019); AIC (660.44) and BIC (665.65) were significantly optimized. This method has improved the prediction robustness of traditional SARIMA models to a certain extent, providing an effective solution for predicting high noise traffic data.