AI 中文总结
该研究以金融系统为试验台，应用谱分解将含噪声的金融相关矩阵分离，用NIFTY 200等数据验证，表明结构化成分能再现全矩阵特性，去噪网络的金融网络组织性更强，基于此构建的投资组合表现更优，证明谱去噪可恢复有意义的网络结构。
AI 中文摘要
从金融回报时间序列估计的经验相关矩阵受到有限样本大小产生的统计噪声的污染，掩盖了资产之间的真实相互作用。我们应用谱分解将经验相关矩阵分离为与超过马尔琴科 - 帕斯图尔界的特征值相关的结构化成分和代表统计噪声的随机成分。使用2010 - 2022年NIFTY 200、NIFTY 500和标准普尔500的日回报数据，我们表明仅由10 - 16个本征模构建的结构化成分在去除大多数噪声主导的本征模的同时，再现了全相关矩阵的主要统计特性。从结构化成分导出的金融网络比从全矩阵或随机矩阵构建的网络表现出显著更强和更稳定的核心 - 外围组织。度保持随机化、柯尔莫哥洛夫 - 斯米尔诺夫和瓦瑟斯坦距离测试证实了结构化和随机成分之间存在明显的统计分离。我们进一步表明结构化网络在印度市场显示出明显的无标度度分布。作为实际应用，基于去噪网络的外围资产构建的投资组合在风险调整基础上始终优于基于未过滤相关性的投资组合和标准基准，通过蒙特卡罗子采样验证了其稳健性。这些结果表明谱去噪有效地从噪声金融相关性中恢复了有意义的网络结构。
英文摘要
Empirical correlation matrices estimated from financial return time series are contaminated by statistical noise arising from finite sample size, obscuring genuine interactions among assets. We apply spectral decomposition to separate the empirical correlation matrix into a structured component associated with eigenvalues exceeding the Marchenko-Pastur bounds and a random component representing statistical noise. Using daily returns from the NIFTY 200, NIFTY 500, and S&P 500 over 2010-2022, we show that the structured component, constructed from only 10-16 eigenmodes, reproduces the main statistical properties of the full correlation matrix while removing most noise-dominated eigenmodes. Financial networks derived from the structured component exhibit significantly stronger and more stable core-periphery organization than networks constructed from the full or random matrices. Degree-preserving randomization, Kolmogorov-Smirnov, and Wasserstein distance tests confirm a clear statistical separation between structured and random components. We further show that structured networks display pronounced scale-free degree distributions in the Indian markets. As a practical application, portfolios constructed from peripheral assets of the denoised networks consistently outperform portfolios based on unfiltered correlations and standard benchmarks on a risk-adjusted basis, with robustness verified through Monte Carlo subsampling. These results demonstrate that spectral denoising effectively recovers meaningful network structure from noisy financial correlations.
