title: Statistical properties of fluctuations of time series representing appearances of words in nationwide blog data and their applications: An example of modeling fluctuation scalings of nonstationary time series.
abstract: To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately 3×10^{9} Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior 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.
authors.affiliation: Hottolink,Inc., 6 Yonbancho Chiyoda-ku, Tokyo 102-0081, Japan.|Risk Analysis Research Center, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan.
authors.forename: Hayafumi
authors.initials: H
authors.lastname: Watanabe
authors.affiliation: Faculty of Engineering, Information and Systems, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305-8573, Japan.
authors.forename: Yukie
authors.initials: Y
authors.lastname: Sano
authors.affiliation: Sony Computer Science Laboratories, 3-14-13 Higashi-Gotanda, Shinagawa-ku, Tokyo 141-0022, Japan.
authors.forename: Hideki
authors.initials: H
authors.lastname: Takayasu
authors.affiliation: Institute of Innovative Research, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan.
authors.forename: Misako
authors.initials: M
authors.lastname: Takayasu