Long-term correlations and multifractality of toll-free calls in China

In the recent decades, calling activities have been studied from different perspectives in social physics field. In diverse studies, call frequencies and call durations have been widely used to quantify calling activity. However, they have been rarely studied. In this work, long-term correlations as well as the multifractality of toll-free call frequency (TFCF) and toll-free call duration (TFCD) time series were investigated with multifractal detrended fluctuation analysis (MFDFA). The results show that these two time series have a similar crossover, which is approximately 36 h, and they have different long-term correlations as well as sophisticated multifractality below and above the crossover. The TFCF time series below the crossover is non-stationary and small fluctuations contribute more to its strong multifractality than large fluctuations. The TFCF time series above the crossover is stationary with long-term anti-correlation and its weak multifractality is only caused by small fluctuations. The TFCD time series below the crossover is non-stationary and large fluctuations contribute more to its strong multifractality than small fluctuations. The TFCD time series above the crossover is stationary with longterm correlation and its weak multifractality is mainly caused by small fluctuations. Moreover, we found that the multifractality of the TFCF time series is primarily caused by correlations, but that of the TFCD time series is caused by a combination of correlations and broad distribution of data. We also discussed the possible factors in the sophisticated multifractality with comparative analysis. (C) 2020 Elsevier B.V. All rights reserved.