对股票市场波动的矩阵H理论方法
Luan M T de Moraes1, Antônio M S Macêdo1, Raydonal Ospina2
1Universidade Federal de Pernambuco, Laboratório de Física Teórica e Computacional, Departamento de Física, Recife, 50670-901 Pernambuco, Brazil.
Physical review. E
|April 18, 2025
概括
矩阵H理论分析复杂的股票市场行为,使用层次的随机过程. 这一框架对标普500指数数据有效,增强了对市场波动和投资组合策略的理解.
科学领域:
- 量化金融 量化金融
- 统计物理 统计物理
- 金融计量经济学 金融计量经济学
背景情况:
- 金融市场的集体行为往往来自复杂的多变量随机过程.
- 层次结构和跨不同时间尺度的相关性是市场动态的关键特征.
- 现有的模型可能无法完全捕捉这些因素的复杂相互作用.
研究的目的:
- 介绍矩阵H理论,一种用于分析多变量随机过程中的集体行为的新框架,具有层次结构.
- 为描述市场信号的联合分布及其基础背景动态提供数学形式主义.
- 为了证明矩阵H理论对现实世界金融市场数据的适用性.
主要方法:
- 模拟变量的联合分布作为大规模多变量和背景分布的化合物.
- 通过内部自由度的层次化随机演变来表征背景.
- 使用Meijer G函数与矩阵参数来描述两个普遍性类 (Wishart和反Wishart) 内的概率分布.
主要成果:
- 矩阵H理论成功地模拟了市场信号和背景波动的联合分布.
- 该理论确定了Wishart和逆Wishart的普遍性类,以简要地描述分布.
- 对标普500指数每日回报的实证分析证实了该理论在描述市场波动方面的有效性.
结论:
- 矩阵H理论为理解金融中的多变量等级过程提供了一个强大的框架.
- 这些发现有助于更深入地了解股票市场动态.
- 该理论对开发改进的投资组合管理策略有潜在的影响.
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