Abstract: The prediction of stock price has always been a hot issue in the financial field, but the volatility and uncertainty of relevant index data make it difficult. Therefore, for a nonlinear and multi-factor-influencing stock system, the traditional forecasting method cannot accurately express the law of stock price changes, and the forecasting effect is poor. Aiming at the complex stock price forecasting problem, this paper establishes a high-order ordinary differential equation model based on Multi-Factor Regularization GEP（MFR-GEP） algorithm, and uses numerical difference to fit the stock price data, and adds other indexes as the regular terms. Here, the index correlation is used to determine the regular term weight parameters, and the principle of fuzzy rough sets is used to determine the sub-function mapping. The model can describe the trend of stock price changes and the data fluctuations. In addition, the regular items allow the model to be predicted based on multiple indicators, avoiding problems such as low accuracy due to single indicator prediction. Finally, the standard GEP algorithm and the traditional prediction algorithm are selected for comparison experiments. The results fully verify the effectiveness and accuracy of the proposed algorithm.

Key words: ordinary differential equation, gene expression programming, multi-index regularization, fuzzy rough set, stock price prediction

摘要： 股价预测一直是金融投资领域的热点问题，但是股票市场相关指标数据的波动性和不确定性使得股价预测问题成为难点。因此对于非线性且受到多因素影响的股票系统，传统的预测方法无法准确地表达股价的变化规律，预测效果较差。针对复杂的股价预测问题，建立了基于多指标正则化GEP算法（Multiple Factor Regularization Gene Expression Programming，MFR-GEP）的高阶常微分方程模型，利用数值差分拟合股价数据，并且加入影响股价的其他指标作为正则项，其中利用指标相关性确定正则项权重参数，应用模糊粗糙集的原理确定子函数映射。该模型能够刻画股价随时间的变化趋势，更好地描述数据波动，正则项的加入使得模型可以根据多指标进行预测，避免因单一指标引起的预测精度低等问题。最后将提出的算法与标准GEP算法及传统预测算法进行对比实验，结果充分验证了该算法的有效性和准确性。

关键词: 常微分方程, 基因表达式编程, 多指标正则化, 模糊粗糙集, 股价预测