股票指数能够反映股票市场总体水平，如果能准确的预测股票指数的走势，不仅有利于政府或监管机构制定更有效的调控政策，也能帮助投资者实现更好的投资表现。由于高噪声、非平稳等特点，股票指数价格预测一直是时间序列任务中的挑战，由于股票指数不具备基本的平稳性、独立同分布等统计特性，因此用传统的线性时间模型来预测难度较大，效果也不佳。深度学习模型具有处理大规模数据的能力，也能抽取更深层次数据间的关系，具备更好的非线性预测能力，因此股票指数预测可成为深度学习模型发挥效能的重要领域。
       对比目前在时序分析领域比较成熟的信息挖掘方式。RNN、LSTM等循环神经网络类模型没有根本解决梯度消失或爆炸问题，因此可能出现信息丢失。Transformer采用的注意力机制虽然没有梯度消失或爆炸问题，但是存在许多无效的注意力计算，浪费了部分计算能力。Informer是基于Transformer的变体，针对时序预测任务进行了改进，采取了稀疏注意力机制和自注意力蒸馏机制，降低了时间复杂度，减少了计算成本，同时采取长序列一步式解码输出，提高预测输出效率，因此Informer非常适用于时序分析。
       深度学习模型的超参数对模型性能有重要影响，实际过程中往往凭借人工经验设置或进行反复尝试确定，极其耗费人力成本和时间成本且缺少理论支撑，本文将差分进化算法(DE)加入到Informer模型中，作为超参数寻优模块，对Informer的输入序列长度、解码器引导长度、数据维度、多头注意力头数、稀疏注意力参数、学习率六个超参数进行寻优，期望获得模型在金融时序任务中的最优性能，同时在DE算法内部加入了重采样功能，加快算法收敛。考虑到特征之间可能存在相关性，本文还采取了主成分分析法(PCA)对特征进行降维处理，得到最终的正交矩阵作为数据集。本文将PCA模块和DE模块加入到Informer，最终构建了一种新的深度学习模型PCA-DE-Informer来预测沪深300股票指数价格。
       本文选取LSTM、TCN、Transformer作为对比模型，分别作为目前具有代表性的三种信息提取机制：循环网络机制、卷积网络机制与自注意力机制。选取MSE、MAE、MAPE三个评价指标，综合全面的评价各模型的优劣。本文还进行了消融实验，通过逐步删除PCA、DE功能模块，在同样的数据集上进行训练与预测。此外，本文还进行了泛化实验，将模型运用至其他数据集上，最终表明模型不同应用场景都取得了最优的预测结果。最后本文基于预测价格构造了量化交易策略，在预测集窗口时间段进行了回测，结果显示策略取得了最高的收益，体现了模型的实际价值。

       The stock market serves as an indicator of a country's economy. The stock price index is a statistic that measures and reacts to the overall level and trend of the stock. Accurately predicting the trend of the stock index is beneficial for the government or regulatory agencies to formulate more effective regulatory policies. It also helps investors make smarter investment decisions and gain higher returns. Predicting stock index prices has always been a challenging task in Time-Series Analysis due to high levels of noise and non-stationarity. Traditional linear time models are not effective in achieving accurate predictions because stock indices lack basic statistical properties such as stationarity and independent homogeneous distribution. Deep learning models can effectively predict stock indexes due to their ability to handle large-scale data, extract deeper data features, and process nonlinear information.
       When comparing the more mature information mining methods in the field of time series analysis to recurrent neural network-like models such as RNN and LSTM, it is evident that the latter do not fundamentally solve the problem of gradient vanishing or explosion, which may result in information loss. While the attention mechanism adopted by Transformer does not have this issue, it does have many ineffective attention computations that waste computational power. Informer is a variant of Transformer that has been optimized for time series prediction. It achieves this by adopting ProbSparse Self-attention and Self-attention Distilling, which reduce time complexity and computational costs. Additionally, it uses generating long sequential outputs through one forward procedure to improve prediction efficiency. Therefore, Informer is highly suitable for Time-Series Analysis.
       The hyperparameters of a deep learning model have a significant impact on its performance. Typically, the process of setting these parameters is determined through repeated attempts and manual experience, which can be extremely costly in terms of both time and manpower. Furthermore, this process often lacks theoretical support. This paper introduces the Differential Evolutionary Algorithm (DE) as a hyperparameter optimization module for the Informer model. Six hyperparameters, including the input sequence length, decoder bootstrap length, data dimensions, number of multiple attention heads, sparse attention parameter, and learning rate, are optimized to achieve optimal performance in financial time-series tasks. The resampling function is also added inside the DE algorithm to speed up the convergence of the algorithm. The paper also processes the dataset, accounting for potential correlations between input features, by implementing principal component analysis (PCA) to downscale the features and obtain the final orthogonal matrix. The paper introduces a new deep learning model, PCA-DE-Informer, which incorporates PCA and DE modules into the existing Informer model to predict the price of the CSI 300 stock index.
       This paper compares three representative information extraction mechanisms: the recurrent neural network mechanism (LSTM), the convolutional network mechanism (TCN), and the self-attention mechanism (Transformer). The evaluation of each model's advantages and disadvantages is based on three selected indexes: MSE, MAE, and MAPE. This paper conducts ablation experiments by gradually deleting the PCA and DE function modules and training and predicting on the same dataset. Additionally, it conducts generalization experiments by applying the model to other datasets and demonstrates that the model achieves optimal prediction results in different application scenarios. Finally, this paper presents a quantitative trading strategy based on the predicted price. The strategy is backtested in the prediction set window time period, and the results demonstrate that it achieves the highest return. This reflects the actual value of the model.