Quantile Regression Fan

Each curve is a separate quadratic quantile regression of log price against log time: the 0.50 curve is the median trend (fair value), while the 0.01 and 0.99 curves bound the historically cheapest and most euphoric extremes. Unlike a least-squares fit, quantile regression is robust to bubbles — the median curve ignores outliers instead of being dragged by them — and fitting each quantile separately lets the fan be asymmetric, wider above than below, like Bitcoin's actual return distribution.

Every band is fit on the full history and rearranged so curves can't cross. Price touching the lower curves has marked every major bottom; riding the upper curves, every mania phase. The risk metric is literally price's interpolated position between these curves.

This mirrors the methodology ITC now uses in place of its retired logarithmic regression (they describe theirs as a "rearranged asymmetric quadratic quantile regression") — ours is an independent implementation of the same idea, so the exact curves will differ.