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
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
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DOI：
10.1103/physreve.94.052317
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Hayafumi Watanabe;Y. Sano;H. Takayasu;M. Takayasu
中科院分区：
文献类型：
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作者：
Hayafumi Watanabe;Y. Sano;H. Takayasu;M. Takayasu
为了阐明一个代表博客中词汇出现的典型非稳态时间序列波动的非平凡经验统计特性，我们调查了大约3×10^{9}篇日本博客文章，为期六年，并分析了一些相应的数学模型。首先，我们介绍了一个可解的非稳态扩展的随机扩散模型，这可以推导出异构随机博客的行为建模。接下来，我们推导出该模型的时间和系综波动标度的理论表达式，并证明这些表达式可以重现所有的经验标度超过8个数量级。此外，我们表明，该模型可以再现其他统计特性的时间序列表示的博客中出现的话，如功能形式的概率密度和相关性的博客总数。作为应用，我们通过测量1771个基本形容词的波动尺度来量化全国性特殊事件的异常。
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.