Time series forecasting represents a significant and challenging task across various fields. Recently, methods based on mode decomposition have dominated the forecasting of complex time series because of the advantages of capturing local characteristics and extracting intrinsic modes from data. Unfortunately, most models fail to capture the implied volatilities that contain significant information. To enhance the prediction of contemporary diverse and complex time series, we propose a novel time series forecasting paradigm that integrates decomposition with the capability to capture the underlying fluctuation information of the series. In our methodology, we implement the Variational Mode Decomposition algorithm to decompose the time series into K distinct sub-modes. Following this decomposition, we apply the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to extract the volatility information in these sub-modes. Subsequently, both the numerical data and the volatility information for each sub-mode are harnessed to train a neural network. This network is adept at predicting the information of the sub-modes, and we aggregate the predictions of all sub-modes to generate the final output. By integrating econometric and artificial intelligence methods, and taking into account both the numerical and volatility information of the time series, our proposed framework demonstrates superior performance in time series forecasting, as evidenced by the significant decrease in MSE, RMSE, and MAPE in our comparative experimental results.

翻译：时间序列预测是各领域一项重要且具挑战性的任务。近年来，基于模态分解的方法因能捕获数据局部特征并提取内在模式，主导了复杂时间序列的预测研究。然而，大多数模型未能捕获包含重要信息的隐含波动性。为提升对当代多样化复杂时间序列的预测能力，我们提出一种融合分解机制与序列潜在波动信息捕获能力的新型时间序列预测范式。该方法采用变分模态分解算法将时间序列分解为K个独立子模态，随后应用广义自回归条件异方差模型提取这些子模态的波动信息。在此基础上，每个子模态的数值数据与波动信息被联合用于训练神经网络，该网络能够有效预测子模态信息，最终通过聚合所有子模态的预测结果生成最终输出。通过计量经济学与人工智能方法的深度融合，并综合考虑时间序列的数值信息与波动特征，本框架在时间序列预测中展现出优越性能——对比实验结果表明，其MSE、RMSE及MAPE指标均显著降低。