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Indicators/Log Regression Bands
Cycle · Long-term fair value Updated daily · 00:00 UTC

Log Regression Bands.

Price growth fitted to a log curve. Bands above and below tell you where this cycle sits in the long arc.
Mode
Smart DCA ▾
Asset
τ TAO▾
Backtest
1 year▾
Buy zone ≤ Buy zone When the indicator drops to or below this threshold, the strategy doubles its weekly buy (Smart-DCA) or opens a long (Trade). It's the "cheap" regime — time to accumulate.
σ
Trim zone ≥Sell zone ≥ Trim zoneSell zone When the indicator climbs to or above this, the strategy skips the weekly buy and trims 5% of the stack. Stretched regime. When the indicator climbs to or above this, the strategy exits to cash. Distribution regime.
σ
Compare with
— ▾
Signal
Set alert
Smart-DCA edge Trade P&L — —
— more coins vs Flat DCA cumulative return
Capital saved Alpha vs hold — —
less capital required per coin outperformance vs Buy & Hold
Activations Time in market — —
— signals in — weeks —% in cash
Price Fair value Residual —
τao/minal
COMPUTING
τao/minal · onchain · daily aggregates
Allocation rule Now — · in — zone
0 — — —
Buy
When residual ≤ lower threshold → deploy 2× weekly budget (deep value zone vs long-term log fair value).
Hold
When lower < residual < upper → deploy 1× weekly budget (baseline DCA).
Trim Sell
When residual ≥ upper threshold → skip buy and trim 5% (top of the fan, overheated).
Price — Latest close
Fair value — Log-fit midline
Residual — Standard deviations from fit
Risk score — 0 (cheap) → 1 (top)
Alpha vs Hold — Strategy − hold
> +2σ
Far above fair value.

Price is more than two standard deviations above the log-regression line. Bitcoin cycle tops have historically printed in this band. Distribute aggressively; expected forward return is poor.

< −2σ
Far below fair value.

Price is more than two standard deviations below the log-regression line. Bitcoin cycle lows have historically printed here. Capitulation conditions — expected forward return is exceptional.

How to read it
The technique Benjamin Cowen built his career on. Fit a logarithmic curve to all of price history, then measure how far above or below that curve we currently sit. The further from the line, the more extreme the regime.

The math: log(price) = a + b · log(days_since_inception). Solve for a and b by ordinary least squares. The fitted line is the long-term fair-value curve; the residuals form a normal-ish distribution whose standard deviation defines the band widths.

On Bitcoin, cycle tops have printed near +2σ, cycle bottoms near −2σ. The fan tightens over time as the data accumulates and the variance compresses — late-cycle peaks tend to be lower (in σ terms) than early ones. This is the "diminishing returns" effect Cowen talks about constantly.

On a younger asset the fit is looser and the bands are wider — limited cycle history so far. As more data lands, the curve calibrates. Until then, treat the bands as directional rather than precise.

The risk-score row maps residual position to a 0–1 scale (0 = deep value, 1 = cycle top). Useful as a DCA framework: scale-in when risk is low, scale-out when risk is high. The backtest is the discrete version of this — cross-based long/cash flips at ±2σ.