变量顺序多孔介质方程:用于建模标普500和比特币价格回报率的应用
Yaoyue Tang1, Fatemeh Gharari2, Karina Arias-Calluari3
1Modelling and Simulation Research Group, The University of Sydney, Sydney NSW 2006, Australia.
Physical review. E
|March 16, 2024
概括
本研究引入了使用VO q-高斯函数对变量顺序 (VO) 分数福克-普朗克方程的新解决方案. 这些发现增强了金融市场的建模和使用长期记忆的时间序列数据.
科学领域:
- 数学物理 数学物理
- 量化金融 量化金融
- 复杂的系统复杂的系统.
背景情况:
- 分数福克-普朗克方程模型复杂的系统与异常扩散.
- 现有的模型可能对现实世界的金融数据分布缺乏稳定性.
- 变量顺序 (VO) 计算为动态系统提供了更灵活的框架.
研究的目的:
- 导出并呈现1+1 VO非线性分数福克-普朗克方程的特定类别的解决方案.
- 探索这些解决方案在金融经济中的应用,包括股票市场和加密货币.
- 在时间序列中分析与记忆效应相关的异常指数的时间演变.
主要方法:
- 使用VO q-高斯函数制定解决方案.
- 应用这些函数来建模金融系统中的价格回报分布.
- 对异常特征指数及其时间动态的分析.
主要成果:
- 确定了VO分数福克-普朗克方程的新型解类.
- VO q-高斯函数在财务回报分布方面表现出卓越的稳定性.
- 该研究提供了对金融时间序列的长期记忆和自相关性模式的洞察.
结论:
- 开发的VO q-Gaussian解决方案为分析复杂的金融系统提供了强大的工具.
- 这种方法提高了对时间序列数据中的异常动态和记忆效应的理解.
- 这些发现对各种现实应用中的建模和预测有影响.
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