Hello, Group

I just get the pure statistical confirmation that cycles work in finance. To avoid any confusion, I emphasize that I mean a statistical confirmation, the confirmation that can be accepted  by academic/scientific community.

I have calculated cyclical genome for 1000 American stocks:



This periodogram clearly shows that some cycles appear much more often than other cycles. The American stocks "love more" only some special cycles. The criticism from a professional statistician may sound like this: "These peaks are results of some calculational artefact".

Ok, I build the "control group": 1000  artificial price charts where daily price changes are generated by random values. I have got this genome for these 1000 random charts:



As you see, there are no cycles there. We observe a kind of "white noise" where all cycles are equally important/unimportant.
Or, to be more precise, it is "gray noise": the amplitude changes while periods change. It appears as the result of a working spectrum algorithm that applies different methods of how to weight cycles (by using amplitude or stored energy in this cycle or some WFA metrics). In any case, this is Chaos, the algorithm does not generate any cycles, i.e. cycles come from the price chart.

This result does not change our working routine though gives us some peace of mind: our research has a solid ground. It looks like my previous confusion (see https://youtu.be/vpaTYYqvVjw?t=1828) is solved now.
 
Best regards.
Sergey.