Matrix H-theory approach to stock market fluctuations

Luan M. T. de Moraes, Ant\^onio M. S. Macedo, Raydonal Ospina and Giovani L. Vasconcelos

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Abstract: We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal) as a compound of a large-scale multivariate distribution with the distribution of a slowly fluctuating background. The background is characterized by a hierarchical stochastic evolution of internal degrees of freedom, representing the correlations between stocks at different time scales. As in its univariate version, the matrix H-theory formalism also has two universality classes: Wishart and inverse Wishart, enabling a concise description of both the background and the signal probability distributions in terms of Meijer G-functions with matrix argument. Empirical analysis of daily returns of stocks within the S&P500 demonstrates the effectiveness of matrix H theory in describing fluctuations in stock markets. These findings contribute to a deeper understanding of multivariate hierarchical processes and offer potential for developing more informed portfolio strategies in financial markets.

Date: 2025-03
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Published in Phys. Rev. E 111, 034101 (2025)

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