Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data

Fuente: arXiv
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Autori principali: de Moraes, Luan M. T., Macêdo, Antônio M. S., Vasconcelos, Giovani L., Ospina, Raydonal
Natura: Preprint
Pubblicazione: 2025
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author de Moraes, Luan M. T.
Macêdo, Antônio M. S.
Vasconcelos, Giovani L.
Ospina, Raydonal
author_facet de Moraes, Luan M. T.
Macêdo, Antônio M. S.
Vasconcelos, Giovani L.
Ospina, Raydonal
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_14325
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data
de Moraes, Luan M. T.
Macêdo, Antônio M. S.
Vasconcelos, Giovani L.
Ospina, Raydonal
Statistical Finance
Data Analysis, Statistics and Probability
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.
title Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data
topic Statistical Finance
Data Analysis, Statistics and Probability
url https://arxiv.org/abs/2507.14325