Visibility graphs of ground-level ozone time series: A multifractal analysis

Abstract

A recent method based on the concurrence of complex networks and multifractal analyses is applied for the first time to explore ground-level ozone behavior. Ozone time series are converted into complex networks for their posterior analysis. The searched purpose is to check the suitability of this transformation and to see whether some features of these complex networks could constitute a preliminary analysis before the more thorough multifractal formalism.

Results show effectively that the exposed transformation stores the original information about the ozone dynamics and gives meaningful knowledge about the time series. Based on these results, the multifractal analysis of the complex networks is performed. Looking at the physical meaning of the multifractal properties (such as fractal dimensions and singularity spectrum), a relationship between those and the degree distribution of the complex networks is found.

In addition to all the promising results, this novel connection between time series and complex networks can deal with both stationary and non-stationary time series, overcoming one of the main limitations of multifractal analysis. Therefore, this technique can be regarded as an alternative to give supplementary information within the study of complex signals.