## Bitcoin Market Capitalisation Projection

The market capitalisation of bitcoin in some currency is obtained by multiplying the number of bitcoin in existence (the total bitcoin money supply) by the valuation in that currency. The value obtained gives an approximation of the magnitude of the bitcoin economy at a given point in time.

The bitcoin money supply increases by a well defined regular schedule, whereas valuation is determined on exchanges and varies with market sentiment. Historic bitcoin market cap data is available in CSV format at blockchain.info/charts, and can be plotted to observe how market cap has developed over time.

Plotting the data on a linear Y-axis it appears that the data may follow an exponential projection, and thus it is natural to switch to plotting with a logarithmic Y-Axis to clarify the nature of the exponential.

The data plot does not describe a straight line and thus is not generated by an exponential time series. In fact the combination of a seemingly exponential plot on a linear scale and a non-exponential plot on a log scale suggests a sub-exponential time series. Therefore a possible choice for a projection that fits the shape of the data is:

$$ y = e^{{ax}^b} \tag{1} $$

Where $b < 1 $

Manual experimentation with this formula resulted in the projection in figure 1, given by:

$$ a = 4.8 $$ $$ b = 0.2025 $$Where $x$ is the number of days since the start date of 2010-08-18.

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Colin,
April 24th, 2017
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