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Order patterns, their variation and change points in financial time series and Brownian motion

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  • Christoph Bandt

    (University of Greifswald)

Abstract

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.

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  • Christoph Bandt, 2020. "Order patterns, their variation and change points in financial time series and Brownian motion," Statistical Papers, Springer, vol. 61(4), pages 1565-1588, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01171-7
    DOI: 10.1007/s00362-020-01171-7
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    References listed on IDEAS

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    Cited by:

    1. Georgy Sofronov & Martin Wendler & Volkmar Liebscher, 2020. "Editorial for the special issue: Change point detection," Statistical Papers, Springer, vol. 61(4), pages 1347-1349, August.
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    3. Yair Neuman & Yochai Cohen, 2022. "Predicting Change in Emotion through Ordinal Patterns and Simple Symbolic Expressions," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    4. Baolong Ying & Qijing Yan & Zehua Chen & Jinchao Du, 2024. "A sequential feature selection approach to change point detection in mean-shift change point models," Statistical Papers, Springer, vol. 65(6), pages 3893-3915, August.

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