Grey Lotka–Volterra models with application to cryptocurrencies adoption

P. Gatabazi, Jules Clement Mba, E. Pindza and C. Labuschagne

Chaos, Solitons & Fractals, 2019, vol. 122, issue C, 47-57

Abstract: The study uses grey Lotka–Volterra model (GLVM) of two and three dimensions for assessing the interaction between cryptocurrencies. The 2-dimensional study is on Bitcoin and Litecoin while the 3-dimensional study is on Bitcoin, Litecoin and Ripple. Records from 28-April-2013 to 10-February-2018 provide forecasting values for Bitcoin and Litecoin through 2-dimensional GLVM study, while records from 7-August-2013 to 10-February-2018 provide forecasting values of Bitcoin, Litecoin and Ripple through 3-dimensional GLVM study. The behaviour of Bitcoin and Litecoin or both Bitcoin, Litecoin and Ripple in future is proposed by looking at the 100 last forecasting values of n-dimensional GLVM study, n={2,3}. Lyapunov exponents of the 2 and 3-dimensional Lotka–Volterra models reveals that it is a chaotic dynamical system. Plots of 2 and 3-dimensional Lotka–Volterra models for filtered datasets suggest also a chaos. Using the mean absolute percentage error criterion, it was found that the accuracy of the GLVM is better than that of the grey model (GM(1,1)). By analysing the 2-dimensional GLVM, Bitcoin and Litecoin are found in the competition known as mutualism or equivalently a win-win situation where Bitcoin transaction is constant while Litecoin transaction has the increasing trend. The 3-dimensional GLVM analysis evokes however, an increasing trend in transacting both Bitcoin, Litecoin and Ripple where Bitcoin keep relatively higher transaction counts.

Keywords: Grey Lotka–Volterra model; Mean absolute percentage error; Competition; Interactions; Continuous time model; Differential equations; Difference equations (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:122:y:2019:i:c:p:47-57

DOI: 10.1016/j.chaos.2019.03.006

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