Grey Lotka–Volterra models with application to cryptocurrencies adoption. (May 2019)

• Record Type: Journal Article
• Authors: Gatabazi, P.; Mba, J.C.; Pindza, E.; Labuschagne, C.
• Is Part Of: Chaos, solitons and fractals. Volume 122(2019)
• Page Start: 47
• Page End: 57
• Publication Date: 2019-05
• Subjects: Grey Lotka–Volterra model -- Mean absolute percentage error -- Competition -- Interactions -- Continuous time model -- Differential equations -- Difference equations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.03.006
• Languages: English
• ISSNs: 0960-0779

Abstract

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.