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What dynamics govern a time series representing the appearance of words insocial media data? In this paper, we investigate an elementary dynamics, fromwhich word-dependent special effects are segregated, such as breaking news,increasing (or decreasing) concerns, or seasonality. To elucidate this problem,we investigated approximately three billion Japanese blog articles over aperiod of six years, and analysed some corresponding solvable mathematicalmodels. From the analysis, we found that a word appearance can be explained bythe random diffusion model based on the power-law forgetting process, which isa type of long memory point process related to ARFIMA(0,0.5,0). In particular,we confirmed that ultraslow diffusion (where the mean squared displacementgrows logarithmically), which the model predicts in an approximate manner,reproduces the actual data. In addition, we also show that the model canreproduce other statistical properties of a time series: (i) the fluctuationscaling, (ii) spectrum density, and (iii) shapes of the probability densityfunctions.

Ultraslow diffusion in language: Dynamics of appearance of already popular adjectives on Japanese blogs