Order patterns and permutation entropy have become useful tools for studying biomedical, geophysical or climate time series. Here we study day-to-day market data, and Brownian motion which is a good model for their order patterns. A crucial point is that for small lags (1 up to 6 days), pattern frequencies in financial data remain essentially constant. The two most important order parameters of a time series are turning rate and up-down balance. For change points in EEG brain data, turning rate is excellent while for financial data, up-down balance seems the best. The fit of Brownian motion with respect to these parameters is tested, providing a new version of a forgotten test by Bienaymé.

中文翻译：

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金融时间序列和布朗运动中的订单模式及其变化和变化点

顺序模式和排列熵已成为研究生物医学、地球物理或气候时间序列的有用工具。在这里，我们研究日常市场数据和布朗运动，这是他们订单模式的一个很好的模型。一个关键点是，对于小滞后（1 到 6 天），金融数据中的模式频率基本保持不变。时间序列的两个最重要的订单参数是翻转率和上下平衡。对于脑电数据的变化点，周转率很好，而对于金融数据，上下平衡似乎最好。布朗运动与这些参数的拟合得到了测试，提供了 Bienaymé 遗忘测试的新版本。