Modeling bitcoin price dynamics with systems dynamics theory

An electrical circuit, schematic representation
A schematic of a mass, a spring and a damper. Only one direction(degree of freedom) is considered in this model
A step responses of a simple dynamic system
A step response of a simple dynamic system, critically (ζ=1) and overdamped ((ζ>1).
Fitting the three major bubbles assuming an overdamped response, with increasing damping coefficient.
Thermocap multiple model, based on extrapolated roots from bubble of ’11 & ‘13
A dynamic model, showing the last three 4 years.
Table 1: parameters of the model-fit with adapted root λ1
  • Bitcoin price dynamics was modeled with dynamic systems theory. Bitcoin price dynamics can be described with a 2nd order differential equation. The dynamics of the system can be described with an increasing damping coefficient that is directly related to the size of the Bitcoin market.
  • The relevant ‘signal’ in Bitcoin price dynamics is the Thermocap Multiple.
  • The model appears to describe a diminishing drop from peak to bottom.
  • It would be more rational to compare market capitalization with cumulative miner reward. However, fitting of the roots was found to become surprisingly constant, when accounting for increased supply.
  • An explanation has been found for the increased length of bear markets after bubbles, because bitcoin dynamics is clearly dependent on the damping coefficient. As this coefficient increases with every higher price level, the length of the bear market increases with it.
  • In case of a new bubble, with this model, an estimate can be made of the price level as function of time.
  • Above model is not complete. It doesn’t consider the phase where excitation of the bitcoin price dynamics takes place. It might be caused by ‘supply shocks’: the halving of Bitcoin rewards every 4 years. This could be part of a next investigation.
  • Modeling of bitcoin price dynamics assuming underdamped conditions. This approach might be feasible in the peaks in the thermocap before 2011 and during the peak in the middle of 2019.
  • Investigating the same behavior in Gold. However, the “swine-cycle” might have to be accounted for.

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