计算机科学

计算机科学 ›› 2025, Vol. 52 ›› Issue (10): 13-21.doi: 10.11896/jsjkx.250100136

• 数智赋能金融科技前沿 • 上一篇    下一篇

基于拓扑结构特征的投资组合构建研究

李瑞阳, 李庶祎, 杨越溪, 彭楚涵, 邢静雨, 乔高秀   

  1. 西南交通大学数学学院 成都 611756
  • 收稿日期:2025-01-21 修回日期:2025-05-06 出版日期:2025-10-15 发布日期:2025-10-14
  • 通讯作者: 乔高秀(gxqiao@home.swjtu.edu.cn)
  • 作者简介:(2637844500@qq.com)
  • 基金资助:
    中央高校基本科研业务费专项资金(202410613071,2682025ZTPY001);国家自然科学基金(72001180)

Research on Portfolio Construction Based on Topological Structure Features

LI Ruiyang, LI Shuyi, YANG Yuexi, PENG Chuhan, XING Jingyu, QIAO Gaoxiu   

  1. School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Received:2025-01-21 Revised:2025-05-06 Online:2025-10-15 Published:2025-10-14
  • About author:LI Ruiyang,born in 2003,is a member of CCF(No.O3787G).His main research interests include data mining and deep learning.
    QIAO Gaoxiu,born in 1982,Ph.D,associate professor.Her main research interests include time series forecasting,derivatives pricing,machine learning and energy economics.
  • Supported by:
    Fundamental Research Funds for the Central Universities of Ministry of Education of China(202410613071,2682025ZTPY001) and National Natural Science Foundation of China(72001180).

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摘要： 近年来,拓扑数据分析(Topological Data Analysis,TDA)在金融领域的应用逐渐显现出价值。TDA通过持久同调等方法构建复形,能有效量化数据的形状,以便提取数据信息,为时间序列分析,特别是金融时间序列的聚类与投资组合的构建提供了独特优势。基于此,通过采用TDA方法对中国股票市场的时间序列数据进行深入挖掘,结合聚类算法,并将其应用于投资组合的构建,分析其有效性。通过滑动窗口法进行验证,结果表明基于TDA(去噪)聚类的投资组合在回报风险比和稳定性方面表现良好,优于市场整体表现。研究表明,TDA方法可以更有效地挖掘股票数据中的信息,为投资者提供科学依据,从而取得最佳收益。

关键词: 拓扑数据分析, 投资组合, 时间序列, 聚类

Abstract: In recent years,the application of topological data analysis(TDA) in the financial field has gradually demonstrated its value.TDA,through methods such as persistent homology,constructing complexes that effectively quantify the shape of data,facilitating the extraction of data information.This provides unique advantages for time series analysis,particularly in the clustering of financial time series and the construction of portfolios.Based on this,by deeply mining the time series data of China's stock market using TDA methods,combined with clustering algorithms,and applying these insights to portfolio construction,the effectiveness of such approaches is analyzed.The results,validated through the sliding window method,indicate that portfolios constructed based on TDA(denoising) clustering perform well in terms of return-risk ratio and stability,outperforming the overall market.Therefore,the TDA method can more effectively mine information from stock data,providing a scientific basis for investors to optimize returns.

Key words: Topological data analysis,Portfolio,Time series,Clustering

中图分类号: 

  • TP399
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