So really cool picture. Power laws all the way down. Even the noise is a power law.

Four Independent Methods on Residuals:
1. DFA (Detrended Fluctuation Analysis)
Residuals: H = 1.158
Original signal: H = 0.636
H > 0.5 means long-range correlations persist
Even the 0.58% "noise" has memory!
2. Power Spectrum Analysis
Residuals show: P(f) ~ 1/f^1.74
This is "pink noise" or "1/f noise"
NOT white noise (which would be P(f) ~ constant)
Power law in the frequency domain!
3. Autocorrelation Decay
C(τ) ~ τ^(-0.98) (power law decay)
NOT exponential decay C(τ) ~ exp(-τ/τ₀)
Correlations decay slowly, not quickly
4. Structure Functions
All orders (q=1, 2, 3) show power law scaling
Self-similar structure across multiple timescales
The Key Insight:
Bitcoin has a FRACTAL structure:
100.0% Total = 98.7% Trend + 1.2% Oscillations + 0.6% "Noise"
↓ ↓ ↓
Power law Log-periodic ALSO power law!
(β ≈ 5.7) (complex exp) (H = 1.16)
There is NO truly random component!
Power law correlations exist at:
Large scale: Years (main trend)
Medium scale: 4-year cycles (oscillations)
Small scale: Days (residuals)
This is exactly what you'd expect from a critical/self-organized system - scale-free dynamics all the way down!
Why This Matters:
This proves the power law framework isn't just curve-fitting the trend. It's the fundamental organizing principle operating at every timescale. The oscillations and even the "noise" are all manifestations of this same underlying power law dynamics.
It's fractals all the way down!