[R] Discrimination of almost-random time series

[Earl F. Glynn]

"Hans Werner Borchers" <hwborchers at googlemail.com> wrote in message 
news:ab3458980711130852m243ef4d0u655b02e74e786786 at mail.gmail.com...
> I've got some time series representing measurements from a physical
> process, like atomic decay data. These time series look almost
> random, but should hopefully be distinguishable as they were taken
> under different conditions.
>
> I am looking for statistical approaches that are sensitive enough to
> discriminate between such series of measurements. Preferably, there
> are also implementations in R.
>
> Please note that I am not interested in tests of random number
> generators, but on tests that can discriminate time series based on
> statistical (or mining) features. Simple summary tests do not work,
> also some of the simpler non-linear tests failed.

I've used Lomb-Scargle periodograms to look for periodic genes in fairly 
short time series from microarray experiments.

A paper, "Significance testing of periodogram ordinates", Chris Koen, 
Astrophysical Journal, 348:700-702, 1990, makes the case that the 
Lomb-Scargle test really is:

   H1:  the observations do not constitute noise.

Koen's paper goes on to say a different statistical test should be used for 
periodicity.  Perhaps the Lomb-Scargle test is still valid to discriminate 
noise.  You might want to try it with your data.

I've run a number of numerical experiments using Lomb-Scargle, and even when 
the p-values wouldn't keep a statistician happy, the Lomb-Scargle p-values 
"find" non-random periodic series fairly well.

I've never made a package out of my Lomb-Scargle code, but perhaps the R 
code here will get you started:
http://research.stowers-institute.org/efg/2005/LombScargle/R/index.htm

Based on this paper:
http://bioinformatics.oxfordjournals.org/cgi/content/abstract/bti789?ijkey=fD5aAeldrkzz765&keytype=ref

efg

Earl F. Glynn
Scientific Programmer
Stowers Institute for Medical Research