Retweets’ time series analysis using wavelet methods
Recently, there has been numerous evidence of the existence of self-organized critical (SOC) transitions in various online social networks (OSN), including Twitter, and various sociophysical models of SOC transitions have been proposed. Despite this, some problems remained unresolved, for example, those related to the determination of the spectral featers of subcritical and supercritical phases of the information stochastic dynamics aggregated by OSNs. We obtained a time series of the retweets number corresponding to three 2016 United States Presidential Election debates. Next, we performed multifractal analysis of the time series using the wavelet leader method and scalograms analysis for continuous wavelet transform of the time series. Multifractal analysis is needed because scaling exponents for the time series are the nonlinear functions of the moments. It was found that the frequency of stochastic oscillations of retweets corresponds to 1/f noise and is the highest during the first, second and third debates. In the time intervals preceding and following the debate, the oscillation frequencies are reduced to the values approximately corresponding to white noise. As we approach to the start of the debate, there is an increase in the magnitude and frequency of the retweets ’oscillations.