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Detecting and interpreting distortions in hierarchical organization of complex time series

Stanisław Drożdż and Paweł Oświȩcimka
Phys. Rev. E 91, 030902(R) – Published 20 March 2015

Abstract

Hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept. For model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric. Using selected time series representing such diverse phenomena as price changes and intertransaction times in financial markets, sentence length variability in narrative texts, Missouri River discharge, and sunspot number variability as examples, we show that the resulting singularity spectra appear strongly asymmetric, more often left sided but in some cases also right sided. We present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying the composition of the time series. One particularly intriguing case of this latter kind of asymmetry is detected in the daily reported sunspot number variability. This signals that either the commonly used famous Wolf formula distorts the real dynamics in expressing the largest sunspot numbers or, if not, that their dynamics is governed by a somewhat different mechanism.

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  • Received 18 December 2014

DOI:https://doi.org/10.1103/PhysRevE.91.030902

©2015 American Physical Society

Authors & Affiliations

Stanisław Drożdż1,2 and Paweł Oświȩcimka1,*

  • 1Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
  • 2Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, Kraków, Poland

  • *pawel.oswiecimka@ifj.edu.pl

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Vol. 91, Iss. 3 — March 2015

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