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Grey Lotka–Volterra models with application to cryptocurrencies adoption

Author

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  • Gatabazi, P.
  • Mba, J.C.
  • Pindza, E.
  • Labuschagne, C.

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.

Suggested Citation

  • Gatabazi, P. & Mba, J.C. & Pindza, E. & Labuschagne, C., 2019. "Grey Lotka–Volterra models with application to cryptocurrencies adoption," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 47-57.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:47-57
    DOI: 10.1016/j.chaos.2019.03.006
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    1. Lakka, Spyridoula & Michalakelis, Christos & Varoutas, Dimitris & Martakos, Draculis, 2013. "Competitive dynamics in the operating systems market: Modeling and policy implications," Technological Forecasting and Social Change, Elsevier, vol. 80(1), pages 88-105.
    2. Joshua R. Hendrickson & Thomas L. Hogan & William J. Luther, 2016. "The Political Economy Of Bitcoin," Economic Inquiry, Western Economic Association International, vol. 54(2), pages 925-939, April.
    3. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
    4. Adrian Blundell-Wignall, 2014. "The Bitcoin Question: Currency versus Trust-less Transfer Technology," OECD Working Papers on Finance, Insurance and Private Pensions 37, OECD Publishing.
    5. Wang, Hsi-Tse & Wang, Ta-Chung, 2016. "Application of the grey Lotka–Volterra model to forecast the diffusion and competition analysis of the TV and smartphone industries," Technological Forecasting and Social Change, Elsevier, vol. 106(C), pages 37-44.
    6. Duan, Hong-Bo & Zhu, Lei & Fan, Ying, 2014. "A cross-country study on the relationship between diffusion of wind and photovoltaic solar technology," Technological Forecasting and Social Change, Elsevier, vol. 83(C), pages 156-169.
    7. Cerqueti, Roy & Tramontana, Fabio & Ventura, Marco, 2015. "On the coexistence of innovators and imitators," Technological Forecasting and Social Change, Elsevier, vol. 90(PB), pages 487-496.
    8. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    9. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    10. Lin, Chiun-Sin, 2013. "Forecasting and analyzing the competitive diffusion of mobile cellular broadband and fixed broadband in Taiwan with limited historical data," Economic Modelling, Elsevier, vol. 35(C), pages 207-213.
    11. Marasco, A. & Picucci, A. & Romano, A., 2016. "Market share dynamics using Lotka–Volterra models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 49-62.
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