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.

利用VMD-LSTM-GARCH模型，将时间序列分解为子模式，并从这些子模式中提取波动率信息，然后利用长期短期记忆网络对每个子模式进行预测，最后将所有子模式的预测结果进行聚合，通过集成计量经济学和人工智能方法，考虑时间序列的数字和波动率信息，该模型在时间序列预测中具有优越的性能。

使用VMD-GARCH-LSTM模型进行时间序列预测的非线性方法