Dynamics of cryptocurrency time-series generation as a fragmentation stochastic process

Abstract

The changes in the price of Bitcoin (BTC) is a stochastic process similar to the foreign exchange market values. In this paper, we suppose that the BTC price is a ratio of two currencies with market values that move in a stochastic fashion. Ratios of two random numbers resulting from stochastic processes can be modelled using a fragmentation model. We use the fragmentation model to identify the dynamical causes of the resulting probability distributions of the magnitude of change in price exhibited a power-law tail and roll-over regime. Consequently, it was found out that if the rate of generation U is described by a gamma function, then it must have a shape parameter k = 1. Moreover, if the degree of generation $V$ is described by another gamma function, then it has a shape parameter k = 3.5.