Those charts really show me what the basic concept in cycle analysis. This is similar to graduate level signal analysis in electrical engineering I've taken. What I did about a year ago was design a bandpass filter to scan the market for dominant frequencies. What I initially saw were imperfect sinusoids. The phases would would change, and the amplitudes would decay in an envelope within about 5 cycles. In building an adaptive filter, the system's natural frequencies will be locked on. These stratgies work as long as the system is linear time-invariant.
The Federal Reserve did a study with an adaptive filter to help them in their planning. Even though they concluded there was no predictive value beyond 2 years, it was a great first guess. The reason longer timeframes are difficult to track is that the financial system's natural tendencies are constantly changing.
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