A broad and widely used class of stationary, linear, additive time series models can have statistical properties which many authors have asserted imply that the underlying process must be non-linear, non-stationary, multiplicative, or inconsistent with shot noise. This result is demonstrated with exact and numerical evaluation of the model flux distribution function and dependence of flux standard deviation on mean flux (here and in the literature called the \emph{rms-flux relation}). These models can: (1) exhibit normal, log-normal or other flux distributions; (2) show linear or slightly non-linear rms-mean flux dependencies; as well as (3) match arbitrary second order statistics of the time series data. Accordingly the above assertions cannot be made on the basis of statistical time series analysis alone. Also discussed are ambiguities in the meaning of terms relevant to this study -- \emph{linear}, \emph{stationary} and \emph{multiplicative} -- and functions that can transform observed fluxes to a normal distribution as well or better than the logarithm.

中文翻译：

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天文时间序列分析研究。七、关于非线性、均方根-平均通量关系和对数正态通量分布的调查

一类广泛且广泛使用的平稳、线性、加性时间序列模型可能具有统计特性，许多作者断言这些特性意味着基础过程必须是非线性、非平稳、乘法或与散粒噪声不一致。该结果通过模型通量分布函数的精确和数值评估以及通量标准偏差对平均通量的依赖性（此处和文献中称为 \emph{rms-flux 关系}）来证明。这些模型可以： (1) 表现出正态、对数正态或其他通量分布；(2) 显示线性或略微非线性的 rms-mean 通量依赖性；以及（3）匹配时间序列数据的任意二阶统计量。因此，上述断言不能仅基于统计时间序列分析。