Hi @Srid, yes indeed I hope that you will find you can discuss these concepts here. They are very fascinating. From my perspective I can explain what Sentient Trader does when it is calculating Sigma L. In fact there are two separate approaches to Sigma L in ST. the first is a fairly generic and non-mathematical approach, where it considers the time displacement in the cycles, and calculates what is called a “Sigma L component” for each cycle. And so for instance if the 40 day cycle has time translation to the right, then clearly there is a strongly bullish underlying trend, but if the sum of the longer cycles does not add up to such a strongly bullish underlying trend, then the Sigma L component for that cycle will be positive to account for the difference. The idea here is that something is causing the bullish distortion in the cycle, which is not accounted for in the longer cycles in the analysis, and therefore it is attributed to “Sigma L”.
In the case of the Composite Model Line, a different approach is taken to calculating Sigma L. What the software does is it calculates the amplitude of each wave of each cycle, and constructs the CML model by simply adding them up. Then it compares the result to the actual price action, and builds a smoothed line which is Sigma L. Some very interesting things emerged when I started working on this. For instance there are shorter frequency fluctuations in the Sigma L line. As others have pointed out, this shouldn’t happen, because Sigma L should be the combination of all longer cycles and therefore it should not have shorter frequency fluctuations. For some time I played around with isolating and eliminating these shorter frequencies, but I found it more effective to leave them in, which is why the Sigma L component of the CML is not strictly speaking “Sigma L”. It is in fact a combination of all the longer cycles (Sigma L) and also all unknown influences on price. For a while I played around with separating these elements and calling the second component “Unknown L”. That all became very complicated for the user, and not really of much use, and so I combined them again. In any case the separating of them was fairly artificial, and didn’t work very well.
The fascinating part of all of this, as you mention in your post is that it is possible to extract the Sigma L line from the CML, and to perform a cyclic analysis on that line.
As a matter of interest, I have a theory as to why there are shorter term fluctuations, which has to do with the fact that we expect the cycles that we analyze to be synchronized in their troughs or their peaks. Where these shorter term fluctuations arise I believe is when there is a shift between the synchronisation of troughs and peaks, and therefore our cyclic model using an analysis which takes a fixed approach to the synchronisation of the turns results in periods of time where the shorter term cycles emerge in the Sigma L line.