A Falsificationist Cycle Analysis of Cryptocurrencies

For more than half a century, the cycle analysis of markets has produced rich conceptual frameworks that have rarely been subjected to empirical falsification. The three historical schools — classical American (Hurst), Italian (battleplan and inverse cycle) and quantitative DSP (Ehlers) — are adopted as alternative doctrines, almost never tested jointly on a statistically relevant sample. This work formalizes a Popperian protocol that puts each founding claim of the three schools to the test on a multi-asset dataset — Bitcoin, Ethereum and Solana since 2017, extended to thirty-seven instruments in six classes and to six stock indices with up to ninety-nine years of daily history — over several thousand phased hierarchical cycles.

The methodology is causal by construction and deterministic; both properties are formalized in automated tests and demonstrated empirically, in particular on the Bayer-tongue detection module, verified as non-repainting in walk-forward mode on five asset/timeframe combinations. To this scaffolding the protocol adds four requirements, which are the part of the work that outlives the individual results: the null value of a measure must be measured, not assumed, with surrogate series that preserve the power spectrum and destroy the temporal structure; a conditional rate must be accompanied by its own marginal, that is, by the same condition counted on the cases the event does not select; a negative outcome does not count until it has been shown that the test would recognize the phenomenon if it were there; and every level must be measured on the timeframe that resolves it, because the daily timeframe does not separate the shortest levels of the hierarchy and measuring them there changes the very numbers under discussion.

The results refute the most exposed canonical assertions: Hurst's fixed harmonic nesting and the principle of harmonicity — the latter with a test whose power is verified on a true synthetic scale, where none of the markets with enough peaks turns out to be closer to the rungs than a set of periods drawn at random from the same grid —, the sequential mean-reversion of durations, Bayer's canonical threshold for connecting cycles, the peak hold, and — by tautology — two claims of the Italian school: the inverse cycle, whose operational definition is not falsifiable ex ante, and the unconditional swing, whose success condition is true in all the measured parent cycles, with and without a swing. They confirm, with statistical significance and cross-asset convergence, the cyclic commonality of durations — strong at the short levels and, on long history, equally strong at the high levels —, cyclical translation as a predictor of polarity, the violation of the previous peak and, in a rewritten form that eliminates a set-theoretic inclusion, the two bearish signals of the Italian corpus.

The same yardstick applies to the regularities the work could claim as its own, and there it is more severe. The short-cycle tail, measured against one hundred phase-randomized surrogates and one hundred AAFT per market, does not leave the cloud in any of the fifteen combinations of asset and level, and at the intermediate levels the observed value lies below the surrogates' median: it is what the detector produces, not what the market does. The same holds for the deviation from the nominal period and for the position of the peak within the cycle. And the work's starting axiom falls too, according to which a quaternary structure would be a binary of binaries: the trough that would separate the two binaries is the lowest of the three internal ones in 1.3% of the 557 measured cycles, against 33.3% for pure indifference — and within the band that the same detector produces on noise.

The contribution is threefold: a falsifiable and reproducible protocol applied uniformly to the whole corpus, regardless of the origin of the assertion; the demonstration of causality and non-repainting of the central analytical component; and the systematic distinction between what the market produces and what the detector produces, which on several occasions changes the sign of a conclusion — to the point of removing, among the regularities this work could have claimed as its own, those that seemed most solid.