  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.
