BTC_POWER_LA

The Power Law Slope Signal to Noise ratio wants to get out of this transition zone to bullish behavior.
Just saying.

Updated log-periodic model with confidence level to 1 sigma.
I wouldn’t put too much weight on the exact values of the tops and bottoms, but the timing may be more meaningful. According to the model, the next bottom is around August of this year.
What I find compelling about this approach is that it uses a single power law with a complex exponent, rather than imposing an external cycle. In this framework, the oscillatory behavior emerges naturally from the data itself as part of the power-law structure.
The model fits the data well up to the present. The key question, as always, is whether th

There is something almost absurd about it, once you see it.
Even when Bitcoin's price deviates from the reference power law — trading above or below the central trend — it tends to move parallel to it.
The trajectory shifts, but the slope holds.
This is because what matters is not where you are on the chart, but which direction you are moving.
The power law defines a direction in log-space. And Bitcoin, stubbornly, keeps moving in that direction.

Several people noticed that the log-periodic model doesn't catch the current drawdown. I asked if a 6th peak could explain it. But it doesn't.
The 5-peak damped model predicts the current price at ~$156k — the actual is ~$71k, a gap of 0.28 dex.
Adding the 6th component (ω ≈ 5.15, corresponding to a longer sub-harmonic cycle with λ ≈ 3.4) improves the overall R² marginally from 0.751 to 0.797, but at the current moment it makes the prediction worse, not better — it actually pushes the model to predict ~$175k.
Two possible interpretations, none of which require adding parameters:
1) Pure nois

If you add a damping term then the model is really good.

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 histo

Bitcoin is not a bubble—it is the opposite: an anti-bubble.
The physicist Didier Sornette showed that financial bubbles exhibit log-periodic oscillations that accelerate as a system approaches a critical point—a crash. The oscillations compress in time, becoming faster and more unstable as the market moves toward collapse.
Bitcoin also displays log-periodic behavior, but with a fundamental difference.
In Sornette’s framework, the log-periodicity is anchored to a finite critical time (the crash), and the oscillations are driven by the system’s proximity to that point. As time progresses, everyt

Let me explain this. You see how the 3 peaks structure repeats itself in the top panel but it is stretched over time?
Do you see how it looks perfectly repeating when you plot on the x axis the log of time instead of time?
This is what log periodic means, Bitcoin is not periodic in time but periodic in the log of time, exactly how it is a straight line not in time but in the log of time.

Of course as we add more and more frequencies we tend to overfit based on past data but it is interesting these frequencies are harmonics of the main one so one could in theory add them in a natural way.
Also this works so much better in a log periodic spectrum than a linear one.

Even just adding more pure harmonics of the main frequency does a pretty good job.
This is really cool.