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的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因能捕捉局部特征并从数据中提取固有模态，在复杂时间序列预测中占据主导地位。然而，多数模型未能捕捉包含重要信息的隐含波动性。为提升对当前快速演变且波动剧烈的时间序列的预测能力，我们提出一种新型分解-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，随后通过GARCH模型提取这些子模态的波动信息作为LSTM的输入。利用各子模态的数值信息与波动信息训练长短期记忆网络，该网络预测子模态后，我们聚合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与波动信息，本模型在时间序列预测中展现出优越性能——对比实验结果表明，MSE、RMSE和MAPE指标均显著降低。