This paper combines discrete wavelet transform (DWT), autoregressive moving average (ARMA), and XGBoost algorithm to propose a weighted hybrid algorithm named DWTs-ARMA-XGBoost (DAX) on long-time temperature series analysis. Firstly, this paper chooses the temperature data of February 1 to 20 from 1967 to 2016 of northern mountainous area in North China as the observed data. Then, we use 10 different discrete wavelet functions to decompose and reconstruct the observed data. Next, we build ARMA models on all the reconstructed data. In the end, we regard the calculations of 10 DWT-ARMA (DA) algorithms and the observed data as the labels and target of the XGBoost algorithm, respectively. Through the data training and testing of the XGBoost algorithm, the optimal weights and the corresponding output of the hybrid DAX model can be calculated. Root mean squared error (RMSE) was followed as the criteria for judging the precision. This paper compared DAX with an equal-weighted average (EWA) algorithm and 10 DA algorithms. The result shows that the RMSE of the two hybrid algorithms is much lower than that of the DA algorithms. Moreover, the bigger decrease in RMSE of the DAX model than the EWA model represents that the proposed DAX model has significant superiority in combining models which proves that DAX has significant improvement in prediction as well.

中文翻译：

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长期温度序列分析的混合时间序列方法

本文结合离散小波变换 (DWT)、自回归移动平均 (ARMA) 和 XGBoost 算法，提出了一种用于长时间温度序列分析的加权混合算法 DWTs-ARMA-XGBoost (DAX)。首先，本文选取华北北部山区1967-2016年2月1-20日的气温数据作为观测数据。然后，我们使用 10 个不同的离散小波函数来分解和重​​建观测数据。接下来，我们在所有重建数据上构建 ARMA 模型。最后，我们将10种DWT-ARMA（DA）算法的计算结果和观测数据分别作为XGBoost算法的标签和目标。通过XGBoost算法的数据训练和测试，可以计算出混合DAX模型的最优权重和相应的输出。均方根误差 (RMSE) 作为判断精度的标准。本文将 DAX 与等权平均 (EWA) 算法和 10 DA 算法进行了比较。结果表明，两种混合算法的RMSE远低于DA算法。此外，DAX 模型的 RMSE 比 EWA 模型下降幅度更大，表明提出的 DAX 模型在组合模型方面具有显着优势，这证明 DAX 在预测方面也有显着改善。