通过随机游走的序语言揭示振幅分布
Unveiling Amplitude Distributions via the Ordinal Language of Random Walks
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中文总结 AI 辅助
该研究提出利用积分时间序列的序结构，通过随机游走的序模式概率解析表达式，结合数值模拟和金融时间序列验证，实现对非高斯振幅分布的准确表征。
中文摘要 AI 辅助
序模式被广泛用于表征时间序列的时间组织，但通常被认为对数据的振幅分布不敏感。本研究表明，通过考虑积分时间序列的序结构可克服这一局限。我们研究由独立非高斯增量生成的随机游走，并推导其相关的序模式概率的解析表达式。对于对称分布，部分序模式的概率完全由对称性决定，其余模式的概率则明确依赖于增量分布的形状。基于$q$-高斯增量的数值模拟验证了理论预测。我们进一步表明，随机游走的构造本身对非高斯涨落的准确表征起关键作用，不同的中心化过程会显著影响所得的序统计量。最后，我们使用金融时间序列验证所提框架，结果显示积分对数收益率的序分布捕捉到符合三次定律的非高斯特征。
英文摘要
Ordinal patterns are widely used to characterize temporal organization in time series, yet they are often considered insensitive to the amplitude distribution of the data. In this work, we show that this limitation can be overcome by considering the ordinal structure of integrated time series. We investigate random walks generated from independent non-Gaussian increments and derive analytical expressions for the ordinal pattern probabilities associated with them. We show that for symmetric distributions, the probabilities of some ordinal patterns are fully determined by symmetry arguments, while those for the remaining patterns depend explicitly on the shape of the increments distribution. Numerical simulations based on $q$-Gaussian increments validate the theoretical predictions. We further show that the construction of the random walk itself plays a fundamental role in the accurate characterization of non-Gaussian fluctuations, as different centering procedures may significantly affect the resulting ordinal statistics. Finally, we validate the proposed framework using financial time series, showing that the ordinal distributions of integrated logarithmic returns capture non-Gaussian features consistent with a cubic law.
