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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (3): 41-48.doi: 10.6040/j.issn.1671-9352.0.2023.526

• 金融数学 • 上一篇    下一篇

基于改进递归图技术的股指市场有效性

刘桂东1,柯宜龙2,尤国桥1*,刘曼茜2   

  1. 1.南京审计大学数学学院, 江苏 南京 211815;2.南京审计大学统计与数据科学学院, 江苏 南京 211815
  • 发布日期:2025-03-10
  • 通讯作者: 尤国桥(1987— ),男,教授,博士,研究方向为计算数学. E-mail:magqyou@nau.edu.cn
  • 作者简介:刘桂东(1991— ),男,讲师,博士,研究方向为计算数学. E-mail:liugd@nau.edu.cn*通信作者:尤国桥(1987— ),男,教授,博士,研究方向为计算数学. E-mail:magqyou@nau.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12371433,12001280);江苏省高校“青蓝工程”;江苏省自然科学基金资助项目(BK20211293);江苏省研究生科研与实践创新计划项目(KYCX23_2259)

Efficiency of stock index market based on improved recurrence plot

LIU Guidong1, KE Yilong2, YOU Guoqiao1*, LIU Manxi2   

  1. 1. School of Mathematics, Nanjing Audit University, Nanjing 211815, Jiangsu, China;
    2. School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, Jiangsu, China
  • Published:2025-03-10

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摘要： 提出一种改进的递归图技术,用于计算基于递归微态的熵值(entropy based on recurrence microstates, ENRM)。该方法使用滚动窗口的方式来遍历递归矩阵的子矩阵,能够在保证原有算法精度的基础上大幅提高计算效率,通过Logistic模型进行模拟实验。结果表明,基于该改进递归图技术的模型具有更高的计算效率和精度。此外,ENRM关于市场有效性的研究结果表明,使用ENRM与传统的递归图指标递归熵(entropy, ENTR)相结合来分析市场有效性时,不仅具有ENTR单指标量化市场有效性的作用,还能有效识别并进行市场有效性呈动态性演化的时间段。

关键词: 递归图, 递归微态的熵, 滚动窗口, 市场有效性

Abstract: An enhanced computational model is introduced for the entropy based on recurrence microstates(ENRM), which builds upon the original method and employs an improved approach involving the traversal of submatrices using a rolling window. This improved computational model significantly improves computational efficiency while maintaining the accuracy of the original algorithm. For simulation experiments, a logistic model is employed, and the results prove that this improved computational model has higher computational efficiency and accuracy. Furthermore, research findings on market efficiency suggest that using the entropy based on recurrence microstates(ENRM)in combination with the traditional recurrence plot metric, entropy(ENTR), not only retains the ability of ENTR to quantify market efficiency but also effectively identifies and analyzes periods during which market efficiency undergoes dynamic evolution.

Key words: recurrence plot, entropy based on recurrence microstates, rolling window, market efficiency

中图分类号: 

  • O24
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