Matrix H-theory approach to stock market fluctuations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910870350594048 |
|---|---|
| author | de Moraes, Luan M. T. Macedo, Antônio M. S. Ospina, Raydonal Vasconcelos, Giovani L. |
| author_facet | de Moraes, Luan M. T. Macedo, Antônio M. S. Ospina, Raydonal Vasconcelos, Giovani L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix H-theory approach to stock market fluctuations de Moraes, Luan M. T. Macedo, Antônio M. S. Ospina, Raydonal Vasconcelos, Giovani L. Statistical Finance 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. |
| title | Matrix H-theory approach to stock market fluctuations |
| topic | Statistical Finance |
| url | https://arxiv.org/abs/2503.08697 |