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 forecasting of current, rapidly evolving, and volatile time series, we propose a novel decomposition-ensemble paradigm, the VMD-LSTM-GARCH model. The Variational Mode Decomposition algorithm is employed to decompose the time series into K sub-modes. Subsequently, the GARCH model extracts the volatility information from these sub-modes, which serve as the input for the LSTM. The numerical and volatility information of each sub-mode is utilized to train a Long Short-Term Memory network. This network predicts the sub-mode, and then we aggregate the predictions from all sub-modes to produce the output. By integrating econometric and artificial intelligence methods, and taking into account both the numerical and volatility information of the time series, our proposed model 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中一项重要且具有挑战性的任务。近年来，基于模态分解的方法凭借其捕捉局部特征和从数据中提取内在模态的优势，主导了复杂时间序列的预测。然而，大多数模型未能捕捉含有重要信息的隐含波动率。为增强对当前快速演变且波动剧烈的时间序列的预测能力，我们提出一种新颖的分解-集成范式——VMD-LSTM-GARCH模型。该模型采用变分模态分解算法将时间序列分解为K个子模态，随后利用GARCH模型从这些子模态中提取波动信息，并将其作为LSTM的输入。基于每个子模态的数值信息和波动信息训练长短期记忆网络，由该网络预测子模态，最后汇总所有子模态的预测结果生成最终输出。通过融合计量经济学与人工智能方法，并综合考虑时间序列的数值信息与波动信息，本模型在时间序列预测中展现出卓越性能，对比实验结果表明其均方误差（MSE）、均方根误差（RMSE）和平均绝对百分比误差（MAPE）均显著降低。