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Multiscale structure of time series revealed by the monotony spectrum

Călin Vamoş*

  • “T. Popoviciu” Institute of Numerical Analysis, Romanian Academy, P.O. Box 68, 400110 Cluj-Napoca, Romania

  • *cvamos@ictp.acad.ro
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Phys. Rev. E 95, 033310 – Published 22 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.033310

Abstract

Observation of complex systems produces time series with specific dynamics at different time scales. The majority of the existing numerical methods for multiscale analysis first decompose the time series into several simpler components and the multiscale structure is given by the properties of their components. We present a numerical method which describes the multiscale structure of arbitrary time series without decomposing them. It is based on the monotony spectrum defined as the variation of the mean amplitude of the monotonic segments with respect to the mean local time scale during successive averagings of the time series, the local time scales being the durations of the monotonic segments. The maxima of the monotony spectrum indicate the time scales which dominate the variations of the time series. We show that the monotony spectrum can correctly analyze a diversity of artificial time series and can discriminate the existence of deterministic variations at large time scales from the random fluctuations. As an application we analyze the multifractal structure of some hydrological time series.

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Phys. Rev. E 95, 033310– Published 22 March, 2017
  • Received 6 April 2016
  • Revised 20 February 2017

©2017 American Physical Society

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