多尺度回报的统计分布和:一个粗的分析和证据,为一个新的风格化的事实
Alejandro Raúl Hernández-Montoya1,2
1Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Campus Sur, Calle Paseo No 112, Lote 2, Colonia Nueva Xalapa, Xalapa 91097, Veracruz, Mexico.
Entropy (Basel, Switzerland)
|February 27, 2026
概括
金融时间序列展示价格运行或趋势. 在DJIA和IPC指数中分析这些趋势,可以发现具有独特统计属性的"趋势回报" (TReturns),从而提供更清晰的市场视图.
科学领域:
- 量化金融 量化金融
- 金融市场的统计分析.
- 复杂的系统复杂的系统.
背景情况:
- 金融时间序列经常显示单调价格变动的时期,称为价格运行或趋势.
- 这些趋势代表了重要的市场行为,可以分析以获得更深入的见解.
研究的目的:
- 识别和分析道斯工业平均线 (DJIA) 和价格和报价指数 (IPC) 中的价格走势.
- 根据这些已识别的趋势,构建和描述一组新的多尺度回报,称为趋势回报 (TReturns).
- 调查这些TReturns的统计和信息特性.
主要方法:
- 在1990年1月2日至2025年10月17日的每日DJIA和IPC指数数据中识别价格走势.
- 趋势回报 (TReturns) 的构建,其中时间尺度是由每个运行周期的指数分布持续时间定义的.
- 对TR回报分布的实证分析,包括中心指数衰变和功率定律尾巴.
- 信息性质的评估使用香农,变量和基于压缩的复杂性.
主要成果:
- TReturns的分布表现出一个中心指数衰变和功率定律尾巴,这种模式在其他复杂系统中观察到.
- 香农随着粗粒度的增加而增加,这表明回报值的范围更广.
- 变显著下降,突出了潜在的时间结构,而压缩比则有所改善,表明随机性减少.
结论:
- TReturns提供了一种非任意的方法来分析多个规模的金融市场行为.
- 这种方法有效地过了微观噪声,揭示了结构化的时间模式.
- TReturns为理解市场动态提供了一个互补的视角,并表现出复杂系统的特征.
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