金融市场中的领滞关系：多种聚类算法的比较
Lead-Lag Relationships in Financial Markets: A Comparison of Multiple Clustering Algorithms
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中文总结 AI 辅助
本文针对领滞关系聚类算法的局限性，引入MiniRocket-KMeans等三种算法并与DTW-KMedoids比较，通过确定最佳聚类数量提升稳定性，验证了领滞交易策略的统计有效性。
中文摘要 AI 辅助
领滞关系广泛应用于金融时间序列，基于该关系已开发出多种聚类算法。传统的DTW-KMedoids算法在合成数据集和真实金融数据集上均表现良好，但仍存在若干局限性：时间复杂度高导致效率低，DTW距离的数学性质较差，聚类效果对聚类数量敏感。为解决上述问题并提升性能，本文引入三种聚类算法：MiniRocket-KMeans、KShape、集成算法（KShape与DTW-KMedoids的组合），并在相同交易策略下，将它们与DTW-KMedoids算法在合成股票数据集和真实股票数据集上的性能进行比较。此外，本文还通过最大化各聚类算法的轮廓系数来确定最佳聚类数量，以提升实验结果的稳定性。主要结论如下：MiniRocket-KMeans在领策略下表现最佳，夏普比率达到0.866，最大回撤控制在-63.9%；集成算法展现出优异的稳定性；确定最佳聚类数量后，鲁棒性显著提升；所有策略夏普比率的假设检验p值均为0.0，验证了领滞交易策略的统计有效性。最后，提出了定制领滞矩阵、优化集成投票机制等未来改进方向。
英文摘要
Lead-lag relationships are widely used in financial time series, and many clustering algorithms based on them have been developed. The traditional DTW-KMedoids algorithm performs well both on the synthetic dataset and the real financial dataset. However, there are still several limitations to these algorithms: low efficiency caused by high time complexity, poor mathematical properties from DTW distance, the clustering effect is sensitive to the number of clusters. To solve the problems above and improve the performance, this paper introduces three clustering algorithms: MiniRocket-KMeans, KShape, Ensemble algorithm (a combination of KShape and DTW-KMedoids) and compares their performance on synthetic and real stock datasets with DTW-KMedoids algorithm under the same trade strategy. In addition, this paper also finds the best number of clusters by maximizing the silhouette coefficient in each clustering algorithm to improve the stability of the experiment results. Our main conclusions are as follows: MiniRocket-KMeans performs best under the lead strategy, achieving a Sharpe ratio of 0.866 with a maximum drawdown controlled at -63.9\%; the ensemble algorithm exhibits excellent stability; the robustness is significantly improved after finding the best number of clusters; the p-values of the hypothesis test on the Sharpe ratio of all strategies are 0.0, verifying the statistical validity of the lead-lag trading strategy. Finally, future improvement directions such as customized lead-lag matrices and optimized ensemble voting mechanisms are proposed.
