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Forecasting Mid-price Movement of Bitcoin Futures Using Machine Learning

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  • Akyildirim, Erdinc

    (Department of Mathematics, ETH, Zurich, Switzerland and University of Zurich, Department of Banking and Finance, Zurich, Switzerland and Department of Banking and Finance, Burdur Mehmet Akif Ersoy University, Burdur, Turkey)

  • Cepni, Oguzhan

    (Department of Economics, Copenhagen Business School)

  • Corbet, Shaen

    (DCU Business School, Dublin City University, Dublin 9, Ireland and School of Accounting, Finance and Economics, University of Waikato, New Zealand)

  • Uddin, Gazi Salah

    (Department of Management and Engineering, Linköping University, 581 83 Linköping, Sweden)

Abstract

In the aftermath of the global financial crisis and on-going COVID-19, investors face challenges in understanding price dynamics across assets. In this paper, we explore the applicability of a large scale comparison of machine learning algorithms (MLA) to predict mid-price movement for bitcoin futures prices. We use high-frequency intra-day data to evaluate the relative forecasting performances across various time-frequencies, ranging between 5-minutes and 60-minutes. The empirical analysis is based on six different specifications of MLA methods during periods of pandemic. The empirical results show that MLA outperforms the random walk and ARIMA forecasts in Bitcoin futures markets, which may have important implications in the decision-making process of predictability.

Suggested Citation

  • Akyildirim, Erdinc & Cepni, Oguzhan & Corbet, Shaen & Uddin, Gazi Salah, 2020. "Forecasting Mid-price Movement of Bitcoin Futures Using Machine Learning," Working Papers 20-2020, Copenhagen Business School, Department of Economics.
  • Handle: RePEc:hhs:cbsnow:2020_020
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    1. Dimitrios Koutmos, 2020. "Market risk and Bitcoin returns," Annals of Operations Research, Springer, vol. 294(1), pages 453-477, November.
    2. Atsalakis, George S. & Atsalaki, Ioanna G. & Pasiouras, Fotios & Zopounidis, Constantin, 2019. "Bitcoin price forecasting with neuro-fuzzy techniques," European Journal of Operational Research, Elsevier, vol. 276(2), pages 770-780.
    3. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CIRJE F-Series CIRJE-F-1078, CIRJE, Faculty of Economics, University of Tokyo.
    4. Vasilios Plakandaras & Theophilos Papadimitriou & Periklis Gogas, 2015. "Forecasting Daily and Monthly Exchange Rates with Machine Learning Techniques," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(7), pages 560-573, November.
    5. Kim, A. & Yang, Y. & Lessmann, S. & Ma, T. & Sung, M.-C. & Johnson, J.E.V., 2020. "Can deep learning predict risky retail investors? A case study in financial risk behavior forecasting," European Journal of Operational Research, Elsevier, vol. 283(1), pages 217-234.
    6. Sánchez Lasheras, Fernando & de Cos Juez, Francisco Javier & Suárez Sánchez, Ana & Krzemień, Alicja & Riesgo Fernández, Pedro, 2015. "Forecasting the COMEX copper spot price by means of neural networks and ARIMA models," Resources Policy, Elsevier, vol. 45(C), pages 37-43.
    7. Yongmei Fang & Bo Guan & Shangjuan Wu & Saeed Heravi, 2020. "Optimal forecast combination based on ensemble empirical mode decomposition for agricultural commodity futures prices," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(6), pages 877-886, September.
    8. Sensoy, Ahmet, 2019. "The inefficiency of Bitcoin revisited: A high-frequency analysis with alternative currencies," Finance Research Letters, Elsevier, vol. 28(C), pages 68-73.
    9. Shaen Corbet & Charles Larkin & Brian M. Lucey & Andrew Meegan & Larisa Yarovaya, 2020. "The impact of macroeconomic news on Bitcoin returns," The European Journal of Finance, Taylor & Francis Journals, vol. 26(14), pages 1396-1416, September.
    10. Chowdhury, Reaz & Rahman, M. Arifur & Rahman, M. Sohel & Mahdy, M.R.C., 2020. "An approach to predict and forecast the price of constituents and index of cryptocurrency using machine learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    11. Akyildirim, Erdinç & Corbet, Shaen & Cumming, Douglas & Lucey, Brian & Sensoy, Ahmet, 2020. "Riding the Wave of Crypto-Exuberance: The Potential Misusage of Corporate Blockchain Announcements," Technological Forecasting and Social Change, Elsevier, vol. 159(C).
    12. Yinghao Chen & Xiaoliang Xie & Tianle Zhang & Jiaxian Bai & Muzhou Hou, 2020. "A deep residual compensation extreme learning machine and applications," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(6), pages 986-999, September.
    13. Wittkemper, Hans-Georg & Steiner, Manfred, 1996. "Using neural networks to forecast the systematic risk of stocks," European Journal of Operational Research, Elsevier, vol. 90(3), pages 577-588, May.
    14. El Shazly, Mona R. & El Shazly, Hassan E., 1999. "Forecasting currency prices using a genetically evolved neural network architecture," International Review of Financial Analysis, Elsevier, vol. 8(1), pages 67-82.
    15. Alameer, Zakaria & Fathalla, Ahmed & Li, Kenli & Ye, Haiwang & Jianhua, Zhang, 2020. "Multistep-ahead forecasting of coal prices using a hybrid deep learning model," Resources Policy, Elsevier, vol. 65(C).
    16. Akhtaruzzaman, Md & Boubaker, Sabri & Sensoy, Ahmet, 2021. "Financial contagion during COVID–19 crisis," Finance Research Letters, Elsevier, vol. 38(C).
    17. Justin A. Sirignano, 2019. "Deep learning for limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 549-570, April.
    18. Matyjaszek, Marta & Riesgo Fernández, Pedro & Krzemień, Alicja & Wodarski, Krzysztof & Fidalgo Valverde, Gregorio, 2019. "Forecasting coking coal prices by means of ARIMA models and neural networks, considering the transgenic time series theory," Resources Policy, Elsevier, vol. 61(C), pages 283-292.
    19. Chai, Jian & Xing, Li-Min & Zhou, Xiao-Yang & Zhang, Zhe George & Li, Jie-Xun, 2018. "Forecasting the WTI crude oil price by a hybrid-refined method," Energy Economics, Elsevier, vol. 71(C), pages 114-127.
    20. Auld, Tom & Linton, Oliver, 2019. "The behaviour of betting and currency markets on the night of the EU referendum," International Journal of Forecasting, Elsevier, vol. 35(1), pages 371-389.
    21. Nicolas Huck, 2019. "Large data sets and machine learning: Applications to statistical arbitrage," Post-Print hal-02143971, HAL.
    22. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CARF F-Series CARF-F-430, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    23. Erdinc Akyildirim & Ahmet Goncu & Ahmet Sensoy, 2021. "Prediction of cryptocurrency returns using machine learning," Annals of Operations Research, Springer, vol. 297(1), pages 3-36, February.
    24. Akyildirim, Erdinc & Corbet, Shaen & Sensoy, Ahmet & Yarovaya, Larisa, 2020. "The impact of blockchain related name changes on corporate performance," Journal of Corporate Finance, Elsevier, vol. 65(C).
    25. Samitas, Aristeidis & Kampouris, Elias & Kenourgios, Dimitris, 2020. "Machine learning as an early warning system to predict financial crisis," International Review of Financial Analysis, Elsevier, vol. 71(C).
    26. Mona Shazly & Hassan Shazly, 1999. "Forecasting currency prices using a genetically evolved neural network architecture," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 5(1), pages 148-148, February.
    27. Jia‐Yen Huang & Jin‐Hao Liu, 2020. "Using social media mining technology to improve stock price forecast accuracy," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 104-116, January.
    28. Paolo Giudici & Gloria Polinesi, 2021. "Crypto price discovery through correlation networks," Annals of Operations Research, Springer, vol. 299(1), pages 443-457, April.
    29. Corbet, Shaen & Cumming, Douglas J. & Lucey, Brian M. & Peat, Maurice & Vigne, Samuel A., 2020. "The destabilising effects of cryptocurrency cybercriminality," Economics Letters, Elsevier, vol. 191(C).
    30. Corbet, Shaen & Hou, Yang & Hu, Yang & Oxley, Les, 2020. "The influence of the COVID-19 pandemic on asset-price discovery: Testing the case of Chinese informational asymmetry," International Review of Financial Analysis, Elsevier, vol. 72(C).
    31. de la Horra, Luis P. & de la Fuente, Gabriel & Perote, Javier, 2019. "The drivers of Bitcoin demand: A short and long-run analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 21-34.
    32. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CARF F-Series CARF-F-441, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    33. Mensi, Walid & Sensoy, Ahmet & Vo, Xuan Vinh & Kang, Sang Hoon, 2020. "Impact of COVID-19 outbreak on asymmetric multifractality of gold and oil prices," Resources Policy, Elsevier, vol. 69(C).
    34. Carol Alexander & Jaehyuk Choi & Heungju Park & Sungbin Sohn, 2020. "BitMEX bitcoin derivatives: Price discovery, informational efficiency, and hedging effectiveness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(1), pages 23-43, January.
    35. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Oxley, Les & Xu, Danyang, 2021. "Pandemic-related financial market volatility spillovers: Evidence from the Chinese COVID-19 epicentre," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 55-81.
    36. Hubáček, Ondřej & Šourek, Gustav & Železný, Filip, 2019. "Exploiting sports-betting market using machine learning," International Journal of Forecasting, Elsevier, vol. 35(2), pages 783-796.
    37. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin Technical Trading with Articial Neural Network," CIRJE F-Series CIRJE-F-1090, CIRJE, Faculty of Economics, University of Tokyo.
    38. Hu, Yang & Hou, Yang (Greg) & Oxley, Les & Corbet, Shaen, 2021. "Does blockchain patent-development influence Bitcoin risk?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 70(C).
    39. Akyildirim, Erdinc & Corbet, Shaen & Katsiampa, Paraskevi & Kellard, Neil & Sensoy, Ahmet, 2020. "The development of Bitcoin futures: Exploring the interactions between cryptocurrency derivatives," Finance Research Letters, Elsevier, vol. 34(C).
    40. Justin Sirignano & Rama Cont, 2019. "Universal features of price formation in financial markets: perspectives from deep learning," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1449-1459, September.
    41. Ghoddusi, Hamed & Creamer, Germán G. & Rafizadeh, Nima, 2019. "Machine learning in energy economics and finance: A review," Energy Economics, Elsevier, vol. 81(C), pages 709-727.
    42. Shu, Min & Zhu, Wei, 2020. "Real-time prediction of Bitcoin bubble crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    43. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    44. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "High frequency volatility co-movements in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 62(C), pages 35-52.
    45. Corbet, Shaen & Larkin, Charles & Lucey, Brian, 2020. "The contagion effects of the COVID-19 pandemic: Evidence from gold and cryptocurrencies," Finance Research Letters, Elsevier, vol. 35(C).
    46. Goodell, John W., 2020. "COVID-19 and finance: Agendas for future research," Finance Research Letters, Elsevier, vol. 35(C).
    47. Conlon, Thomas & Corbet, Shaen & McGee, Richard J., 2020. "Are cryptocurrencies a safe haven for equity markets? An international perspective from the COVID-19 pandemic," Research in International Business and Finance, Elsevier, vol. 54(C).
    48. Philip, R., 2020. "Estimating permanent price impact via machine learning," Journal of Econometrics, Elsevier, vol. 215(2), pages 414-449.
    49. Akyildirim, Erdinc & Corbet, Shaen & Lucey, Brian & Sensoy, Ahmet & Yarovaya, Larisa, 2020. "The relationship between implied volatility and cryptocurrency returns," Finance Research Letters, Elsevier, vol. 33(C).
    50. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    51. Zhang, Guoqiang & Eddy Patuwo, B. & Y. Hu, Michael, 1998. "Forecasting with artificial neural networks:: The state of the art," International Journal of Forecasting, Elsevier, vol. 14(1), pages 35-62, March.
    52. Huck, Nicolas, 2019. "Large data sets and machine learning: Applications to statistical arbitrage," European Journal of Operational Research, Elsevier, vol. 278(1), pages 330-342.
    53. Sharif, Arshian & Aloui, Chaker & Yarovaya, Larisa, 2020. "COVID-19 pandemic, oil prices, stock market, geopolitical risk and policy uncertainty nexus in the US economy: Fresh evidence from the wavelet-based approach," International Review of Financial Analysis, Elsevier, vol. 70(C).
    54. Yarovaya, Larisa & Mirza, Nawazish & Abaidi, Jamila & Hasnaoui, Amir, 2021. "Human Capital efficiency and equity funds’ performance during the COVID-19 pandemic," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 584-591.
    55. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "Volatility spillover effects in leading cryptocurrencies: A BEKK-MGARCH analysis," Finance Research Letters, Elsevier, vol. 29(C), pages 68-74.
    56. Feng Ma & Chao Liang & Yuanhui Ma & M.I.M. Wahab, 2020. "Cryptocurrency volatility forecasting: A Markov regime‐switching MIDAS approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(8), pages 1277-1290, December.
    57. Fan, Liwei & Pan, Sijia & Li, Zimin & Li, Huiping, 2016. "An ICA-based support vector regression scheme for forecasting crude oil prices," Technological Forecasting and Social Change, Elsevier, vol. 112(C), pages 245-253.
    58. Chen, Wei & Xu, Huilin & Jia, Lifen & Gao, Ying, 2021. "Machine learning model for Bitcoin exchange rate prediction using economic and technology determinants," International Journal of Forecasting, Elsevier, vol. 37(1), pages 28-43.
    59. Mahboubeh Faghih Mohammadi Jalali & Hanif Heidari, 2020. "Predicting changes in Bitcoin price using grey system theory," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-12, December.
    60. Corbet, Shaen & Lucey, Brian & Peat, Maurice & Vigne, Samuel, 2018. "Bitcoin Futures—What use are they?," Economics Letters, Elsevier, vol. 172(C), pages 23-27.
    61. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Larkin, Charles & Oxley, Les, 2020. "Any port in a storm: Cryptocurrency safe-havens during the COVID-19 pandemic," Economics Letters, Elsevier, vol. 194(C).
    62. Adamantios Ntakaris & Martin Magris & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2018. "Benchmark dataset for mid‐price forecasting of limit order book data with machine learning methods," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 852-866, December.
    63. Nakano, Masafumi & Takahashi, Akihiko & Takahashi, Soichiro, 2018. "Bitcoin technical trading with artificial neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 587-609.
    64. Wang, Minggang & Tian, Lixin & Zhou, Peng, 2018. "A novel approach for oil price forecasting based on data fluctuation network," Energy Economics, Elsevier, vol. 71(C), pages 201-212.
    65. Adcock, Robert & Gradojevic, Nikola, 2019. "Non-fundamental, non-parametric Bitcoin forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
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    More about this item

    Keywords

    Cryptocurrency; Bitcoin futures; Machine learning; Covid-19; k-Nearest neighbors; Logistic regression; Naive bayes; Random forest; Support vector machine; Extreme gradient; Boosting;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

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