KILLED · no stable cycle
Hypothesis
Markets carry a measurable dominant cycle (Ehlers); estimating its period and phase times entries at cycle troughs and exits at peaks.
Math — dominant period via DFT power
Pick the period maximizing spectral power over a rolling window:
$$ \hat T = \arg\max_{T}\ \Big|\sum_{n} x_n\, e^{-2\pi i n / T}\Big|^{2} $$
Method
Rolling DFT / Hilbert dominant-cycle on 1h bars across 30 symbols, enter on inferred cycle phase, costs applied.
Results
| Dominant period stability | changes every ~30 bars |
| Phase-timed entry Sharpe | 0.1 |
Crypto has no persistent dominant cycle — the estimated period jumps continuously, so phase timing is noise. Cycles fit ex-post on any series; out-of-sample the period is not stable enough to act on.
A spectrum always has a peak. The question is whether that peak is the same one bar from now — for crypto prices, it is not.