标题： 矩阵H理论方法在股票市场波动中的应用 显示英文标题

标题： Matrix H-theory approach to stock market fluctuations

摘要： 我们引入矩阵H理论，这是一种分析具有层次结构的多变量随机过程产生的集体行为的框架。 该理论将多个变量的联合分布（测量信号）建模为大规模多变量分布与缓慢波动背景分布的组合。 背景由内部自由度的层次化随机演化所表征，代表不同时间尺度股票之间的相关性。 与单变量版本类似，矩阵H理论的形式也具有两种普适类：Wishart和逆Wishart，使得能够通过带有矩阵变量的Meijer G函数简洁地描述背景和信号概率分布。 对标准普尔500指数内股票每日收益的实证分析证明了矩阵H理论在描述股市波动方面的有效性。 这些发现有助于更深入地理解多变量层次过程，并为金融市场的更明智投资组合策略的发展提供了潜力。 显示英文摘要

摘要： 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.