论文标题
天文学时间序列分析中的研究：VII。有关非线性，RMS均值通量关系和对数正常通量分布的询问
Studies in Astronomical Time Series Analysis: VII. An Enquiry Concerning Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions
论文作者
论文摘要
广泛而广泛使用的固定，线性，加性时间序列模型可以具有统计属性，许多作者断言，基础过程必须是非线性，非平稳，乘法或与射击噪声不一致的。通过对模型通量分布函数的精确和数值评估，磁通标准偏差对平均通量的依赖性（此处和文献称为\ emph {rms-flux关系}），证明了这一结果。这些模型可以：（1）表现出正常，对数正态或其他通量分布； （2）显示线性或略微非线性RMS均值通量依赖性；以及（3）匹配时间序列数据的任意二阶统计信息。因此，不能仅基于统计时间序列分析来做出上述断言。还讨论了与本研究相关的术语含义的歧义 - \ emph {linear}，\ emph {stastary}和\ emph {乘法} - 以及可以将观察到的磁通转化为正态分布或更好的函数。
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.
