English

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

Statistical Finance 2023-01-02 v1

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.

Keywords

Cite

@article{arxiv.1910.09978,
  title  = {Order patterns, their variation and change points in financial time series and Brownian motion},
  author = {Christoph Bandt},
  journal= {arXiv preprint arXiv:1910.09978},
  year   = {2023}
}