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The Wavelet Scalogram in the Study of Time Series

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Advances in Differential Equations and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 4))

Abstract

Wavelet theory has been proved to be a useful tool in the study of time series. Specifically, the scalogram allows the detection of the most representative scales (or frequencies) of a signal. In this work, we present the scalogram as a tool for studying some aspects of a given signal. Firstly, we introduce a parameter called scale index, interpreted as a measure of the degree of the signal’s non-periodicity. In this way, it can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. Secondly, we introduce a method for comparing different scalograms. This can be applied for determining if two time series follow similar patterns.

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Author information

Authors and Affiliations

  1. Facultad de Economía, Departamento de Matemáticas para la Economía y la Empresa, Universidad de Valencia, Avda. Tarongers s/n, 46022, Valencia, Spain

    Vicente J. Bolós

  2. Departamento de Matemáticas, Centro Universitario de Plasencia, Universidad de Extremadura, Avda. Virgen del Puerto 2, 10600, Plasencia, Spain

    Rafael Benítez

Authors
  1. Vicente J. Bolós
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  2. Rafael Benítez
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Corresponding author

Correspondence to Vicente J. Bolós .

Editor information

Editors and Affiliations

  1. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Fernando Casas

  2. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Vicente Martínez

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Bolós, V.J., Benítez, R. (2014). The Wavelet Scalogram in the Study of Time Series. In: Casas, F., Martínez, V. (eds) Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-06953-1_15

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