To match a curve created from Metcalfe's Law with the data and prevent autocorrelation, a regression model that acts as a generalized difference equation ln(𝑌𝑡) − 𝜌ln(𝑌𝑡−1) = 𝑎0(1 − 𝜌) + 𝛽0 (ln(𝑋𝑡) −  𝜌ln( 𝑋𝑡 −1))+ 𝑢𝑡  (where 𝑌𝑡 = bitcoin price) is used.

Lognormal values from Metcalfe's Law in a generalized difference equation

Converting Metcalfe values and Bitcoin values to lognormal forms ensures the accuracy of data associated by eliminating the effect of choice on reference currency. Lognormal values also aid in rectifying any variance in the regression in order to ensure that there is a clear linkage between the law and Bitcoin.

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- Usage of lognormal values to approximate Metcalfe values
- Usage of Gompertz curve to correct Metcalfe's Law

Mitigations of inaccuracies in Metcalfe's Law

 Peterson, Timothy, Metcalfe's Law as a Model for Bitcoin's Value (January 22, 2018). Alternative Investment Analyst Review, Q2 2018, Vol. 7, No. 2, 9-18., Available at SSRN: https://ssrn.com/abstract=3078248 or http://dx.doi.org/10.2139/ssrn.3078248 

Metcalfe's Law as a Model for Bitcoin's Value

Usage of lognormal values to approximate Metcalfe values

Metcalfe's Law can be adjusted in a curve with the data by applying a Gompertz function to address inflation from bitcoin creation.

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