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Weekly Bitcoin prices fitted to the Bitcoin power law, with a four-year halving-cycle log-sine adjustment fit only from prior out-of-sample power-law residuals. Historical adjusted ratios are out-of-sample: the current point is not included in its own sine fit. The adjusted model is listed separately on the Forecasts and mean-reversion pages. The log-sine component can be discontinuous at halving dates because the sine curve assumes exactly four years per cycle, while the actual halving date can arrive earlier or later.

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Bitcoin price with out-of-sample log-sine halving-era power-law model
Bitcoin price with out-of-sample log-sine halving-era power-law model over the prior four years and next four years

Historical ratio of Bitcoin price to out-of-sample power-law fitted price split by halving era, with days into era on the x axis

Historical ratio of Bitcoin price to out-of-sample log-sine-power-law fitted price split by halving era, with days into era on the x axis
Historical Bitcoin power-law R squared from rolling prior fits
Out-of-sample halving-cycle power-law model date versus years until one million dollars per bitcoin

The $1M date can be discontinuous because the halving-cycle adjustment is cyclical: a projection may first reach $1M near the top of one cycle, or if that peak falls short after the fit changes, it may need to wait until the next cycle peak.