Abstract: The difficulty of time series prediction lies in how to handle non-stationarity and volatility. When dealing with non-stationarity, existing deep learning models adopt a method of stabilizing the input sequences before training, which has problems of weak ability to eliminate non-stationarity or loss of information. When dealing with volatility, LSTM models with a single-head attention mechanism are usually used, which have weak ability to capture global dependencies and affect prediction accuracy. To address these issues, in terms of dealing with non-stationarity, a Prophet-CEEMDAN secondary decomposition method that follows the principle of “extraction-decomposition” is proposed. By decomposing the original sequence into a set of components, this method ensures the integrity of trend and periodic characteristics while increasing the proportion of stationary components in the component set, providing more stable data for the prediction model. In terms of volatility, a long short-term memory model with multi-head self-attention mechanism (LSTM-MH-SA) is applied. The LSTM-MH-SA model stacks attention heads in parallel to capture the volatility characteristics of different time periods in the sequence and connect them, improving the ability to capture global volatility information. Combining Prophet CEEMDAN and LSTM-MH-SA, a PCLMS (Prophet-CEEMDAN decomposition and LSTM with multi-head self-attention) model that can simultaneously handle non-stationarity and high volatility in time series is proposed. Experiments on multiple stock datasets and synthetic datasets show that compared with the benchmark model, CNN-LSTM, and Informer models, the PCLMS model has the best average performance in various evaluation indicators and performs best on datasets with high volatility.

Key words: time series prediction, non-stationarity, high volatility, long short-term memory neural network, multi-head self-attention

摘要： 时间序列预测的难点在于如何处理好非平稳性和波动性。在应对非平稳性时，现有深度学习模型在训练前采取平稳化输入序列的方法，存在消解非平稳性能力不强或信息损失的问题；在应对波动性时，通常采用带有单头注意力机制的LSTM模型，捕获全局依赖能力弱，影响预测精度。针对上述问题，在处理非平稳性方面，提出遵循“提取-分解”原则的Prophet-CEEMDAN二次分解法，将原始序列分解为一组分量，该方法在确保趋势和周期特征完整的情况下，提高分量集合中平稳分量的占比，为预测模型提供更稳定的数据分布。在波动性方面，通过使用带有多头自注意力机制的长短期记忆（LSTM-MH-SA）神经网络模型，并行地堆叠注意力头用于捕获序列不同时间段的波动特征并联系起来，提高捕获全局波动信息的能力。结合Prophet-CEEMDAN和LSTM-MH-SA，提出能够同时处理时间序列非平稳性和高波动性的PCLMS模型。在多个股票数据集和合成数据集上的实验表明，对比基准模型、CNN-LSTM和Informer模型，PCLMS模型在各项评价指标的平均值最优，对波动率较高的数据集性能表现最好。

关键词: 时间序列预测, 非平稳, 高波动, 长短期记忆神经网络, 多头自注意力