A Bitcoin price prediction model assuming oscillatory growth and lengthening cycles

Abstract

This article’s motivation is to understand the volatile Bitcoin price increase. The objective is to develop price estimation methods. The methodology is to present five differential equation models estimated against the 23 July 2010–21 June 2021 Bitcoin data. The findings are that Gompertz growth fits the damped oscillations and lengthening cycles well, and tracks the early data better with the weighted least squares method. Gompertz growth combined with charged capacitor growth tracks the early data even better. Logistic growth is too slow to track the early data. Logistic growth combined with charged capacitor growth to some extent tracks the early data. Pure charged capacitor growth is unrealistic. The dates for the future bull market maxima depend to a low degree on the growth model carrying capacity approached asymptotically, assumed to match gold at $10 trillion, and to be 50 times higher. The implications for traders are to focus on the large standard deviations. Investors should understand the growth potential compared with other asset classes. Regulators should ensure financial stability by focusing on the fluctuations. Central banks should adjust the money supply while acknowledging. Bitcoin competition. Collective units should understand Bitcoin growth models to determine whether to accept Bitcoin transactions.

Keywords:

• Bitcoin
• logistic growth
• oscillation
• lengthening cycles
• price prediction
• differential equations
• least squares method

JEL Classification:

• Numbers: C5
• E3

Acknowledgements

We thank three anonymous referees for useful comments, and John F. Moxnes for useful discussions before writing this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The article contains no associated data. All data generated or analyzed during this study is included in this published article.

Notes

1. https://8marketcap.com/metals.  Retrieved February 20, 2022.

2. https://messari.io/asset/bitcoin/historical.  Retrieved February 20, 2022.

3. The Mathematica 13 software package (www.wolfram.com) was used. The codes used for the simulations are available from the authors upon request.

Additional information

Notes on contributors

Guizhou Wang

Guizhou Wang is a PhD student at the University of Stavanger, Norway, since 2020-06. His working PhD thesis title is “Game Theoretic Modeling of Economic Systems Involving Digital Currencies.” He has published 10 articles in peer reviewed journals. His research fields are digital currencies, game theory, risk analysis, cryptocurrencies, central bank digital currencies, econometrics. He holds a MSc degree in financial economics from the University of Chinese Academy of Sciences (Beijing, China), 2016-09 – 2019-06, focusing on mathematical finance, econometrics, venture capital, and cryptocurrency. He holds a BSc degree in finance from the Jinan University (Guangzhou, China), 2010-09 – 2014-06, focusing on finance, derivatives, and mathematical modeling. Email: [email protected].

Kjell Hausken

Kjell Hausken is a professor of economics and societal safety at the University of Stavanger, Norway, since 1999. His research fields are terrorism, societal safety, economics, economic risk management, economics and safety, political economy, information security, public choice, conflict, game theory, reliability, war, crime, risk analysis, disaster prevention, stochastic theory, dynamics, petroleum economics, resilience management. He holds a PhD from the University of Chicago (1990-1994), was a postdoc at the Max Planck Institute for the Studies of Societies (Cologne) 1995-1998, and a visiting scholar at Yale School of Management 1989-1990. He holds a Doctorate Program Degree (HAE) (“Philosophical, Behavioral, and Gametheoretic Negotiation Theory”) in Administration from the Norwegian School of Economics and Business Administration (NHH), a MSc degree in electrical engineering, cybernetics, from the Norwegian Institute of Technology (NTNU), focusing on mathematics and statistics, and a minor in Public Law from the University of Oslo. He has published 270 articles in peer reviewed journals, one book, edited two books, is/was on the Editorial Board for Theory and Decision (May 20, 2007 –), Reliability Engineering & System Safety (January 17, 2012 –), and Defence and Peace Economics (December 4, 2007 – December 31, 2015), has refereed 400 submissions for 85 journals, and advises and has advised seven PhD students. Email: [email protected].