Marchenko-Pastur

Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data ArXiv ID: 2507.14325 “View on arXiv” Authors: Luan M. T. de Moraes, Antônio M. S. Macêdo, Giovani L. Vasconcelos, Raydonal Ospina Abstract We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation matrices in multivariate financial data by considering an informational cascade modeled as a hierarchical structure akin to the Kolmogorov statistical theory of turbulence. Our approach extends the Marchenko-Pastur distribution to account for distinct characteristic scales, capturing a larger fraction of data variance, and challenging the traditional view of noise-dressed financial markets. We conjecture that the effectiveness of our method stems from the increased complexity in financial markets, reflected by new characteristic scales and the growth of computational trading. These findings not only support the turbulent market hypothesis as a source of noise but also provide a practical framework for noise reduction in empirical correlation matrices, enhancing the inference of true market correlations between assets. ...

Signal inference in financial stock return correlations through phase-ordering kinetics in the quenched regime ArXiv ID: 2409.19711 “View on arXiv” Authors: Unknown Abstract Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock return correlation matrix typically aligns with a rescaled Marchenko-Pastur distribution, indicating no detectable signal. In this study, we introduce a stochastic field theory model to establish a detection threshold for signals present in the limit where the eigenvalues are within the continuous spectrum, which itself closely resembles that of a random matrix where standard methods such as principal component analysis fail to infer a signal. We then apply our method to Standard & Poor’s 500 financial stocks’ return correlations, detecting the presence of a signal in the largest eigenvalues within the continuous spectrum. ...