Thanks Simba for the explanation and encouragement, but before I proceed I want to make sure that the cycles are not a figment of the way the price is processed. I would like to ask whether the cyclic components could possibly be the result of aliasing.

GUM1 SPectrum.JPG Let me show you what I mean. Here is GBPUSD M1 and two spectral plots from R_MESA. The first plot is the spectrum of GU M1 with no processing. The second is the spectrum of GU M1 after passing it through an anti aliasing filter designed so that the signal can be sampled at 1 hour intervals without violating Nyquists sampling theorum. If the M1 signal is simply sampled at 1 hour intervals, without first low pass filtering (and that's precisely what the H1 close is), the subsampling process will introduce aliased artifacts. Because the M1 close has significant energy below 120 min period, sampling at 60 min will alias a lot of energy into the H1 samples. All the peaks that show left of 120 minutes will appear as peaks in the H1 spectrum. The location of the peaks can be calculated, but the process is a mess, so I have not done it. Also MESA may not pick up all the aliased energy, like an FFT would.

Now lets look at the spectrum of GU H1 with no anti aliasing filter applied.
GUH1 spectrum.JPG
Where did all those peaks come from? If I was the church lady, I might think it was SATAN... but in fact I think it is aliasing. Perhaps I should subsample the filtered M1 price and look at it's spectrum. But that's for another day.

Incidentally, thanks to RC for the excellent software tools.

Regards... MadCow...
P.S. Think how much more we can alias into the H4 spectrum.