Grey Lotka–Volterra models with application to cryptocurrencies adoption

• Published in: Chaos, solitons and fractals Vol. 122; pp. 47 - 57
• Main Authors: Gatabazi, P., Mba, J.C., Pindza, E., Labuschagne, C.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2019
• Subjects: Competition; Continuous time model; Difference equations; Differential equations; Grey Lotka–Volterra model; Interactions; Mean absolute percentage error; Competition; Grey Lotka–Volterra model; Difference equations; Continuous time model; Differential equations; Interactions; Mean absolute percentage error
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2019.03.006

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.