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Segmentation of time series in up- and down-trends using the epsilon-tau procedure with application to USD/JPY foreign exchange market data

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  • Arthur Matsuo Yamashita Rios de Sousa
  • Hideki Takayasu
  • Misako Takayasu

Abstract

We propose the epsilon-tau procedure to determine up- and down-trends in a time series, working as a tool for its segmentation. The method denomination reflects the use of a tolerance level ε for the series values and a patience level τ in the time axis to delimit the trends. We first illustrate the procedure in discrete random walks, deriving the exact probability distributions of trend lengths and trend amplitudes, and then apply it to segment and analyze the trends of U.S. dollar (USD)/Japanese yen (JPY) market time series from 2015 to 2018. Besides studying the statistics of trend lengths and amplitudes, we investigate the internal structure of the trends by grouping trends with similar shapes and selecting clusters of shapes that rarely occur in the randomized data. Particularly, we identify a set of down-trends presenting similar sharp appreciation of the yen that are associated with exceptional events such as the Brexit Referendum in 2016.

Suggested Citation

  • Arthur Matsuo Yamashita Rios de Sousa & Hideki Takayasu & Misako Takayasu, 2020. "Segmentation of time series in up- and down-trends using the epsilon-tau procedure with application to USD/JPY foreign exchange market data," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-21, September.
    • Handle: RePEc:plo:pone00:0239494
    DOI: 10.1371/journal.pone.0239494
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    1. Peng, C.-K. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Sciortino, F. & Simons, M. & Stanley, H.E., 1992. "Fractal landscape analysis of DNA walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 25-29.
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