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

TL;DR

This study analyzes the statistical properties of word appearance fluctuations in six years of Japanese blog data, introduces a new non-steady diffusion model, and demonstrates its ability to replicate empirical fluctuation scalings and other properties, aiding in event abnormality detection.

Contribution

The paper presents a novel non-steady extension of the random diffusion model that accurately reproduces empirical fluctuation scalings in nonstationary time series of blog word appearances.

Findings

Model reproduces empirical fluctuation scalings over eight orders of magnitude.

Model captures probability density and correlation structures of the data.

Quantifies abnormality of nationwide events using fluctuation scalings of adjectives.

Abstract

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