An Enquiry Concerning Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions

Jan 07, 2020 - 11:00 am to 12:00 pm

Campus, Varian 355

Jeff Scargle (NASA Ames Research Center)

When we entertain any suspicion that a data analysis term is employed without any meaning or idea (as is but too frequent), we need but enquire from what impressions is that supposed idea derived.  Incautious attribution of the term(s) non-)linearity to time series data is meaningless -- a category mistake.  I demonstrate that the simple but powerful linear first order autoregressive process AR(1), (also known as Ornstein-Uhlenbeck or damped random walk process) has a linear rms-mean flux relation over many time scales and may exhibit a log-normal flux distribution -- properties commonly but incorrectly claimed to imply non-linearity, non-statationarity, multiplicativity and the like.

Two transformations of observed fluxes are demonstrated to obey a normal distribution as well as, or better than, log-fluxes.

The relation between time series statistics and physical properties of variable astronomical sources needs to be reevaluated.