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Everything you always wanted to know about bitcoin modelling but were afraid to ask

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  • Fantazzini, Dean
  • Nigmatullin, Erik
  • Sukhanovskaya, Vera
  • Ivliev, Sergey

Abstract

Bitcoin is an open source decentralized digital currency and a payment system. It has raised a lot of attention and interest worldwide and an increasing number of articles are devoted to its operation, economics and financial viability. This article reviews the econometric and mathematical tools which have been proposed so far to model the bitcoin price and several related issues, highlighting advantages and limits. We discuss the methods employed to determine the main characteristics of bitcoin users, the models proposed to assess the bitcoin fundamental value, the econometric approaches suggested to model bitcoin price dynamics, the tests used for detecting the existence of financial bubbles in bitcoin prices and the methodologies suggested to study the price discovery at bitcoin exchanges.

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  • Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2016. "Everything you always wanted to know about bitcoin modelling but were afraid to ask," MPRA Paper 71946, University Library of Munich, Germany, revised 2016.
    • Handle: RePEc:pra:mprapa:71946
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    1. David Garcia & Claudio Juan Tessone & Pavlin Mavrodiev & Nicolas Perony, 2014. "The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy," Papers 1408.1494, arXiv.org.
    2. Stephens-Davidowitz, Seth, 2014. "The cost of racial animus on a black candidate: Evidence using Google search data," Journal of Public Economics, Elsevier, vol. 118(C), pages 26-40.
    3. John Fry, 2014. "Multivariate bubbles and antibubbles," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(8), pages 1-7, August.
    4. Bodart, Vincent & Candelon, Bertrand, 2009. "Evidence of interdependence and contagion using a frequency domain framework," Emerging Markets Review, Elsevier, vol. 10(2), pages 140-150, June.
    5. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    6. D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
    7. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 452-471.
    8. Fantazzini, Dean & Toktamysova, Zhamal, 2015. "Forecasting German car sales using Google data and multivariate models," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 97-135.
    9. Zhou, Wei-Xing & Sornette, Didier, 2008. "Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 243-260.
    10. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    11. Yongchen Zhao, 2021. "The robustness of forecast combination in unstable environments: a Monte Carlo study of advanced algorithms," Empirical Economics, Springer, vol. 61(1), pages 173-199, July.
    12. Vladimir Filimonov & Didier Sornette, "undated". "A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model," Working Papers ETH-RC-11-002, ETH Zurich, Chair of Systems Design.
    13. repec:agr:journl:v:1(590):y:2014:i:1(590):p:103-114 is not listed on IDEAS
    14. Petr Geraskin & Dean Fantazzini, 2013. "Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 366-391, May.
    15. Johansen, Anders, 2003. "Characterization of large price variations in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 157-166.
    16. Zhou, Wei-Xing & Sornette, Didier, 2003. "2000–2003 real estate bubble in the UK but not in the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 249-263.
    17. Cameron, A. Colin & Gelbach, Jonah B. & Miller, Douglas L., 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 238-249.
    18. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
    19. Graf v. Bothmer, Hans-Christian & Meister, Christian, 2003. "Predicting critical crashes? A new restriction for the free variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 539-547.
    20. Zhou, Wei-Xing & Sornette, Didier, 2009. "A case study of speculative financial bubbles in the South African stock market 2003–2006," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 869-880.
    21. Anton Badev & Matthew Chen, 2014. "Bitcoin: Technical Background and Data Analysis," Finance and Economics Discussion Series 2014-104, Board of Governors of the Federal Reserve System (U.S.).
    22. Sornette, Didier & Zhou, Wei-Xing, 2006. "Predictability of large future changes in major financial indices," International Journal of Forecasting, Elsevier, vol. 22(1), pages 153-168.
    23. Ali, Robleh & Barrdear, John & Clews, Roger & Southgate, James, 2014. "The economics of digital currencies," Bank of England Quarterly Bulletin, Bank of England, vol. 54(3), pages 276-286.
    24. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
    25. David Garcia & Claudio Tessone & Pavlin Mavrodiev & Nicolas Perony, "undated". "The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy," Working Papers ETH-RC-14-001, ETH Zurich, Chair of Systems Design.
    26. Ladislav Kristoufek, 2015. "What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-15, April.
    27. Jiang, Zhi-Qiang & Zhou, Wei-Xing & Sornette, Didier & Woodard, Ryan & Bastiaensen, Ken & Cauwels, Peter, 2010. "Bubble diagnosis and prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 149-162, June.
    28. Pavel Ciaian & Miroslava Rajcaniova & d’Artis Kancs, 2016. "The digital agenda of virtual currencies: Can BitCoin become a global currency?," Information Systems and e-Business Management, Springer, vol. 14(4), pages 883-919, November.
    29. Adam Hayes, 2015. "A Cost of Production Model for Bitcoin," Working Papers 1505, New School for Social Research, Department of Economics.
    30. Breitung, Jorg & Candelon, Bertrand, 2006. "Testing for short- and long-run causality: A frequency-domain approach," Journal of Econometrics, Elsevier, vol. 132(2), pages 363-378, June.
    31. David Garcia & Frank Schweitzer, 2015. "Social signals and algorithmic trading of Bitcoin," Papers 1506.01513, arXiv.org, revised Sep 2015.
    32. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    33. Francois R. Velde, 2013. "Bitcoin: a primer," Chicago Fed Letter, Federal Reserve Bank of Chicago, issue Dec.
    34. Jamal Bouoiyour & Refk Selmi, 2015. "What Does Bitcoin Look Like?," Annals of Economics and Finance, Society for AEF, vol. 16(2), pages 449-492, November.
    35. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    36. Jamal Bouoiyour & Refk Selmi & Aviral Kumar Tiwari, 2015. "Is Bitcoin Business Income Or Speculative Foolery? New Ideas Through An Improved Frequency Domain Analysis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-23.
    37. David Yermack, 2013. "Is Bitcoin a Real Currency? An economic appraisal," NBER Working Papers 19747, National Bureau of Economic Research, Inc.
    38. Adam Hayes, 2015. "The Decision to Produce Altcoins: Miners' Arbitrage in Cryptocurrency Markets," Working Papers 1504, New School for Social Research, Department of Economics.
    39. Filimonov, V. & Sornette, D., 2013. "A stable and robust calibration scheme of the log-periodic power law model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3698-3707.
    40. Aaron Yelowitz & Matthew Wilson, 2015. "Characteristics of Bitcoin users: an analysis of Google search data," Applied Economics Letters, Taylor & Francis Journals, vol. 22(13), pages 1030-1036, September.
    41. Zhou, Wei-Xing & Sornette, Didier, 2006. "Is there a real-estate bubble in the US?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 297-308.
    42. Cheah, Eng-Tuck & Fry, John, 2015. "Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin," Economics Letters, Elsevier, vol. 130(C), pages 32-36.
    43. Hasbrouck, Joel, 1995. "One Security, Many Markets: Determining the Contributions to Price Discovery," Journal of Finance, American Finance Association, vol. 50(4), pages 1175-1199, September.
    44. Fantazzini, Dean, 2009. "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2168-2188, April.
    45. Vladimir Filimonov & Didier Sornette, 2011. "A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model," Papers 1108.0099, arXiv.org, revised Jun 2013.
    46. Beat Weber, 2016. "Bitcoin and the legitimacy crisis of money," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 40(1), pages 17-41.
    47. Rainer Böhme & Nicolas Christin & Benjamin Edelman & Tyler Moore, 2015. "Bitcoin: Economics, Technology, and Governance," Journal of Economic Perspectives, American Economic Association, vol. 29(2), pages 213-238, Spring.
    48. Dwyer, Gerald P., 2015. "The economics of Bitcoin and similar private digital currencies," Journal of Financial Stability, Elsevier, vol. 17(C), pages 81-91.
    49. Lin, L. & Ren, R.E. & Sornette, D., 2014. "The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 210-225.
    50. Brandvold, Morten & Molnár, Peter & Vagstad, Kristian & Andreas Valstad, Ole Christian, 2015. "Price discovery on Bitcoin exchanges," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 36(C), pages 18-35.
    51. Stephanie Lo & J. Christina Wang, 2014. "Bitcoin as money?," Current Policy Perspectives 14-4, Federal Reserve Bank of Boston.
    52. Sornette, Didier & Woodard, Ryan & Zhou, Wei-Xing, 2009. "The 2006–2008 oil bubble: Evidence of speculation, and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1571-1576.
    53. Angela ROGOJANU & Liana BADEA, 2014. "The issue of competing currencies. Case study – Bitcoin," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(1(590)), pages 103-114, January.
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    Cited by:

    1. Schilling, Linda & Uhlig, Harald, 2019. "Some simple bitcoin economics," Journal of Monetary Economics, Elsevier, vol. 106(C), pages 16-26.
    2. Julien Chevallier & Dominique Guégan & Stéphane Goutte, 2021. "Is It Possible to Forecast the Price of Bitcoin?," Forecasting, MDPI, vol. 3(2), pages 1-44, May.
    3. Bruno Biais & Christophe Bisière & Matthieu Bouvard & Catherine Casamatta & Albert J. Menkveld, 2023. "Equilibrium Bitcoin Pricing," Journal of Finance, American Finance Association, vol. 78(2), pages 967-1014, April.
    4. Yulin Liu & Luyao Zhang, 2022. "Cryptocurrency Valuation: An Explainable AI Approach," Papers 2201.12893, arXiv.org, revised Jul 2023.
    5. Viviane Naimy & Omar Haddad & Gema Fernández-Avilés & Rim El Khoury, 2021. "The predictive capacity of GARCH-type models in measuring the volatility of crypto and world currencies," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-17, January.
    6. Juneman Abraham & Dian Utami Sutiksno & Nuning Kurniasih & Ari Warokka, 2019. "Acceptance and Penetration of Bitcoin: The Role of Psychological Distance and National Culture," SAGE Open, , vol. 9(3), pages 21582440198, July.
    7. Dean Fantazzini & Stephan Zimin, 2020. "A multivariate approach for the simultaneous modelling of market risk and credit risk for cryptocurrencies," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 47(1), pages 19-69, March.
    8. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    9. Julien Chevallier & Dominique Guégan & Stéphane Goutte, 2021. "Is It Possible to Forecast the Price of Bitcoin?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-04250269, HAL.
    10. Pele, Daniel Traian & Mazurencu-Marinescu-Pele, Miruna, 2019. "Metcalfe's law and herding behaviour in the cryptocurrencies market," Economics Discussion Papers 2019-16, Kiel Institute for the World Economy (IfW Kiel).
    11. Skander Slim & Ibrahim Tabche & Yosra Koubaa & Mohamed Osman & Andreas Karathanasopoulos, 2023. "Forecasting realized volatility of Bitcoin: The informative role of price duration," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(7), pages 1909-1929, November.
    12. Pele, Daniel Traian & Mazurencu-Marinescu-Pele, Miruna, 2018. "Cryptocurrencies, Metcalfe's law and LPPL models," IRTG 1792 Discussion Papers 2018-056, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Zura Kakushadze & Jim Kyung-Soo Liew, 2018. "CryptoRuble: From Russia with Love," Papers 1801.05760, arXiv.org.
    14. Pele, Daniel Traian & Mazurencu-Marinescu-Pele, Miruna, 2019. "Metcalfe's law and log-period power laws in the cryptocurrencies market," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 13, pages 1-26.
    15. Sofoklis Vogiazas & Constantinos Alexiou, 2019. "Bitcoin: The Road to Hell Is Paved With Good Promises," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 48(1), February.
    16. Panagiotidis, Theodore & Stengos, Thanasis & Vravosinos, Orestis, 2019. "The effects of markets, uncertainty and search intensity on bitcoin returns," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 220-242.

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    More about this item

    Keywords

    Bitcoin; Crypto-currencies; Hash rate; Investors' attractiveness; Social interactions; Money supply; Money Demand; Speculation; Forecasting; Algorithmic trading; Bubble; Price discovery.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E51 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Money Supply; Credit; Money Multipliers
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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