缩放时间序列数据的指数:一种机器学习方法
Sebastian Raubitzek1,2, Luiza Corpaci3, Rebecca Hofer2
1Information and Software Engineering Group, TU Wien, Favoritenstrasse 9-11/194, 1040 Vienna, Austria.
Entropy (Basel, Switzerland)
|December 23, 2023
概括
机器学习模型准确地估计了赫斯特指数,在时间序列数据上表现优于传统方法,如重新缩放范围 (R/S) 分析和确定波动分析 (DFA). 这种新的方法增强了金融等领域的长期依赖性分析.
科学领域:
- 时间序列分析时间序列分析
- 统计建模 统计建模
- 机器学习应用 机器学习应用
背景情况:
- 赫斯特指数量化了时间序列数据中的远程依赖.
- 传统的方法,如重新缩放范围 (R/S) 分析和确定波动分析 (DFA) 具有局限性,特别是在微分的莱维运动中.
- 现有的方法通常需要复杂的预处理步骤,如功率频谱计算.
研究的目的:
- 开发一种基于机器学习的新方法,用于准确的赫斯特指数估计.
- 解决传统方法在区分分数列维运动和分数布朗运动方面的局限性.
- 从时间序列数据直接对缩放指数进行连续估计.
主要方法:
- 在已知Hurst指数的合成数据上训练机器学习模型 (LightGBM,MLP,AdaBoost).
- 利用分数布朗运动和分数列维运动来生成数据.
- 从时间序列直接估计缩放指数,没有功率光谱分析.
主要成果:
- 机器学习估计器显著超过传统的R/S分析和DFA.
- 拟议的方法显示出卓越的准确性,特别是对于类似于分数莱维运动的数据.
- 对财务数据的验证揭示了与文献的差异,但证实了该方法与已知的基本事实相对准确.
结论:
- 机器学习为Hurst指数估计提供了一个强大而准确的替代方案.
- 这种方法通过将机器学习与传统金融方法相结合,推进时间序列分析.
- 这些发现为分析复杂的时间序列数据以更高的精度开辟了新的途径.
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