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

Christoph Bandt ()
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Christoph Bandt: University of Greifswald

Statistical Papers, 2020, vol. 61, issue 4, No 10, 1565-1588

Abstract: 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.

Keywords: Order pattern; Time series; Permutation entropy; Stock data; 62M10; 91B84; 60G18 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00362-020-01171-7

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