Studies in Astronomical Time Series Analysis: VII. An Enquiry Concerning
  Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions
  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.
