基于最大相关熵准则回归模型的大盘指数预测  

Prediction of Market Index Based on Maximum Correlation Entropy Criterion Regression Model

作　　者：李瑛 高胜寒 高雅婷 段鹏 LI Ying;GAO Shenghan;GAO Yating;DUAN Peng(School of Computer Science and Technology,Shandong Technology and Business University,Yantai 264005;School of Statistics,Shandong Technology and Business University,Yantai 264005)

机构地区：[1]山东工商学院计算机科学与技术学院,烟台264005 [2]山东工商学院统计学院,烟台264005

出　　处：《系统科学与数学》2023年第1期186-198,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金面上项目(61772319);国家自然科学基金面上项目(62176140);国家自然科学基金面上项目(61773244);山东省社会科学规划研究一般项目(21CGLJ24);山东工商学院博士启动基金项目(BS202126)资助课题。

摘　　要：大盘指数是衡量股票市场运行情况的“晴雨表”,是投资者洞察股票市场发展态势和制定投资策略的重要依据.大盘指数的变化趋势与经济发展状况、宏观经济政策、投资者心态等诸多复杂因素密切相关,具有明显的随机性和不确定性,这导致精准预测大盘指数的变化趋势成为一个富有挑战性的问题.文章基于最大相关熵准则,使用一种新的回归预测模型,该方法将实际输出与理想输出视为两个随机变量,并采用相关熵度量它们之间的相似程度,进而基于最大熵准则构建一种新的回归模型优化函数,用于指导回归系数的确定.在实际操作中,通常基于有限样本,采用高斯核函数的Parzen窗方法估计两个随机变量的相关熵,因此可借助高斯核函数的核宽调节,解决最小均方误差准则回归模型对异常数据和随机噪声敏感性问题,从而提升预测精度.基于实测数据的实验结果表明:与自回归模型、差分自回归模型以及深度学习方法等相比,文章所提方法能有效降低异常数据对预测精度的影响,预测误差小,鲁棒性强.The market index is a"barometer"to measure the operation of the stock market.It is an important basis for investors to have an insight into the development trend of the stock market and formulate investment strategies.The change trend of the market index is closely related to many complex factors such as national economic development,national macroeconomic policies and investor mentality.It has obvious randomness and uncertainty,so it is still a challenging problem to accurately predict its change trend.In this paper,a new regression prediction model is proposed based on the maximum correlation entropy criterion.In this method,the actual output and ideal output are regarded as two random variables,and the correlation entropy is used to measure the similarity between them.Then,based on the maximum entropy criterion,a new regression model optimization function is constructed to guide the determination of regression coefficients.In practice,the Parzen window method of Gaussian kernel function is usually used to estimate the correlation entropy of two random variables based on limited samples.Therefore,the sensitivity of the least mean square error criterion regression model to abnormal data and random noise can be solved by adjusting the kernel width of Gaussian kernel function,so as to improve the prediction accuracy.The experimental results based on measured data show that compared with autoregressive model,differential autoregressive model and deep learning method,the proposed method can effectively reduce the impact of abnormal data on prediction accuracy,with small prediction error and strong robustness.

关 键 词：最小均方误差 自回归模型 最大相关熵 大盘指数 高斯核函数 PARZEN窗 

分 类 号：F832.51[经济管理—金融学] O212.1[理学—概率论与数理统计]