Your understanding is correct.

Let's fast-forward and say you get the discovery and detection tools you want. And then you discover that there is a persistent cycle for some wide-enough period which can be detected reliably. And there is enough time remaining to take advantage of it before it disappears.
How do you take advantage of it?

• Sell at the peaks of a smoothed BandPass(Price, C, 0.5) and buy at the valleys?
• Synthesize the cycle independently from the series, using sin(Phase)?