Statistical properties of fluctuations of time series representing the appearance of words in nationwide blog data and their applications: An example of observations and the modelling of fluctuation scalings of nonstationary time series

摘要

To elucidate the non-trivial empirical statistical properties of fluctuationsof a typical non-steady time series representing the appearance of words inblogs, we investigated approximately five billion Japanese blogs over a periodof six years and analyse some corresponding mathematical models. First, weintroduce a solvable non-steady extension of the random diffusion model, whichcan be deduced by modelling the behaviour of heterogeneous random bloggers.Next, we deduce theoretical expressions for both the temporal and ensemblefluctuation scalings of this model, and demonstrate that these expressions canreproduce all empirical scalings over eight orders of magnitude. Furthermore,we show that the model can reproduce other statistical properties of timeseries representing the appearance of words in blogs, such as functional formsof the probability density and correlations in the total number of blogs. As anapplication, we quantify the abnormality of special nationwide events bymeasuring the fluctuation scalings of 1771 basic adjectives.