ETH: Power-Law Quantile Bands
Ethereum Power-Law Quantile Bands: daily data through 8 Nov 2026.
Power-law lines through the ETH price history: quantile regressions of the price against the days since Ethereum's genesis block, both on logarithmic scales, at the 1st, 5th, 25th, 50th, 75th, 95th and 99th percentiles.
Why use it. A coin whose price grows as a power of its age draws a straight line on log-log axes. Quantile lines put the price among its own history: below the 5% line it has rarely been cheaper for its age, above the 95% line rarely dearer. How to read it. Read the price against the lines. The median line is the trend. A model fitted to history describes that history; it does not predict prices, and the coin's trend is younger and less settled than Bitcoin's.
Calculation. For each level q: the line log10(price) = a + b × log10(days since 30 July 2015) that minimises the q-weighted absolute distances, over the 3,800 daily closes from 7 August 2015 to 31 December 2025. 1%: a = −5.889, b = 2.493; 5%: a = −6.150, b = 2.616; 25%: a = −5.586, b = 2.525; 50%: a = −4.652, b = 2.289; 75%: a = −2.820, b = 1.812; 95%: a = −1.788, b = 1.586; 99%: a = −1.449, b = 1.516. Time is counted from Ethereum's genesis block (30 July 2015); our ETH/USD index starts a week later, so the fit covers the whole traded history. Refitted once a year on every close up to 31 December of the year before (2026 coefficients), then the whole history is redrawn with the new fit. Daily closes are the published ETH daily price chart (CryptoKeyhole's own index of public exchange markets). Lines are drawn for every day at its closing boundary; the position and deviation use the closes and, for the open day, its latest hourly close. Recomputed every half hour.