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Could we have seen this coming?
Fitting a repeating pattern from just three cycles is genuinely hard. Think of trying to identify the rhythm of a song from hearing only three beats — you can make a reasonable guess, but you won't be certain. That is roughly the situation here.
Yet something important shows up in the Figure below. The spectrum computed from Bitcoin data up to mid-2018 — before the 2021 cycle even began — already shows the same dominant frequency we recover from the full fifteen years of data. The fundamental oscillation was already clearly encoded in the first half of the history. The log-periodic structure is not something that emerges only in hindsight.
A model built from that 2018 data and projected forward gets the amplitude wrong — the early cycles were unusually large, so the model overshoots. But it gets the rhythm right in two ways that matter. It correctly anticipates that the 2022 cycle would be weak and messy, lacking the sharp single peak of previous bull markets — which is exactly what happened, with Bitcoin making two modest attempts at a high rather than one clean one. And it places the next strong cycle well after 2025. As of early 2026, no significant price surge above the long-run trend has occurred — consistent with what the model projected eight years ago.
Getting the amplitude wrong is a real limitation. But getting the timing and the shape of the cycle right — including predicting a quiet 2026 before ever seeing it — is not nothing.