Bitcoin Power Law Mean Reversion Math
Ornstein–Uhlenbeck (OU) process, continuous-time “damped spring” model
Bitcoin’s long-run “fair value” follows a power law in time (log(FV_t) = a + b·log(t)). Price wanders around this trend, but the deviation tends to decay back toward zero.
Key quantities
d_t = log(P_t) − log(FV_t)
z_t = d_t / σ (σ = residual std dev)
Model (the backbone)
Treat deviations as an AR(1) / OU-like process:
d_{t+1} = φ d_t + ε_{t+1}, with |φ| < 1
E[d_{t+k} | d_t] = d_t · φ^k
Mean reversion speed
ρ(k) ≈ e^(−λk), with λ = −ln(φ)
Half-life h = ln(2)/λ ≈ 133 days ⇒ φ ≈ 2^(−1/133) ≈ 0.995 per day
Practical meaning (Feb 2026)
The “pricing error” shrinks roughly exponentially:
50% closes in ~4–5 months (1 half-life)
75% closes in ~9 months (2 half-lives)
90% closes in ~14–15 months (~3.3 half-lives)
Physical analogy
Damped spring: restoring pull ∝ −dt, noise shocks = ε.
Bottom line
Bitcoin behaves like a noisy, slow mean-reverting process around its power-law trend. Bigger |z| today implies stronger expected pull toward trend value over the next 6–18 months.
#FOMO #Reversion #Correction #CalculationGuide #TradeHalt
