在非静止时间序列中时间波动缩放指数的演变,使用随机动力学的超对称理论
1Universidad Nacional de Colombia, Departamento de Física, Bogotá D.C. 111321, Colombia.
Physical review. E
|March 16, 2024
概括
本研究引入了一种新方法,用于理解复杂系统中的时间波动缩放 (TFS). 该方法准确地模拟了金融市场的波动性,为市场不确定性提供了洞察力.
科学领域:
- 复杂系统科学 复杂系统科学
- 统计物理 统计物理
- 金融数学 金融数学
背景情况:
- 时间波动缩放 (TFS) 描述了复杂系统 (Ξ2∼M1^α_TFS) 中的差异与平均值的关系.
- TFS在金融,流行病学和计数过程中具有应用,但其起源和动态演变尚未完全理解.
- 现有的模型缺乏一个框架来解释非静止时间序列中TFS指数的时间演变.
研究的目的:
- 为了理解TFS的起源,扩展路径积分形式主义.
- 在非静止时间序列中分析TFS指数 (α_TFS(t)) 的时间演变.
- 为量化复杂系统中的不确定性和波动性提供理论基础.
主要方法:
- 使用巴里西-索拉斯方法扩展路径积分形式主义.
- 在累积生成函数中引入非线性项以建模任意时刻演变.
- 使用累积生成函数 (n∈{1,2}) 的线性组合来复制TFS的模型的开发.
- 对TFS指数的时间演变的分析表达式的推导,α_TFS(t).
主要成果:
- 建立了一个新的理论框架来描述实证时间序列中平均值 (M1(t)) 和方差 (Ξ2(t)) 的演变.
- 导出和验证了时间依赖的TFS指数α_TFS(t的分析表达式.
- 该模型准确地捕捉了金融时间序列 (股票指数和货币对) 中的平均值和差异动态.
- 证实TFS指数是不确定性和波动性的量化指标.
结论:
- 路径积分形式主义的提议扩展成功地解释了TFS的起源和时间演变.
- 对α_TFS(t) 的衍生分析表达式为分析非静止时间序列提供了强大的工具.
- 这些发现对金融市场的风险管理和波动性预测有重大影响.
- 这项工作提供了一种统一的方法来理解各种复杂系统中新出现的缩放性质.
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