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

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  • Christoph Bandt

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 Bienaym'e.

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  • Christoph Bandt, 2019. "Order patterns, their variation and change points in financial time series and Brownian motion," Papers 1910.09978, arXiv.org.
    • Handle: RePEc:arx:papers:1910.09978
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    References listed on IDEAS

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