Time Series Forecasting of Bitcoin Price Based on Autoregressive Integrated Moving Average and Machine Learning Approaches

Document Type : Original Article


1 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

2 Daniel J. Epstein department of industrial and systems engineering, University of Southern California, Los Angeles, United States


Bitcoin as the current leader in cryptocurrencies is a new asset class receiving significant attention in the financial and investment community and presents an interesting time series prediction problem. In this paper, some forecasting models based on classical like ARIMA and machine learning approaches including Kriging, Artificial Neural Network (ANN), Bayesian method, Support Vector Machine (SVM) and Random Forest (RF) are proposed and analyzed for modelling and forecasting the Bitcoin price. While some of the proposed models are univariate, the other models are multivariate and as a result, the maximum, minimum and the opening daily price of Bitcoin are also used in these models. The proposed models are applied on the Bitcoin price from December 18, 2019 to March 1, 2020 and their performances are compared in terms of the performance measures of RMSE and MAPE by Diebold-Mariano statistical test. Based on RMSE and MAPE measures, the results show that SVM provides the best performance among all the models. In addition, ARIMA and Bayesian approaches outperform other univariate models where they provide smaller values for RMSE and MAPE.


1. Bontempi, G., Ben Taieb, S., and Le Borgne, Y. A., Machine Learning Strategies for Time Series Forecasting. European Business Intelligence Summer School, Vol. 138, (2012), 62-77. doi: 10.1007/978-3-642-36318-4_3
2. Stock, J. H. and Watson, M. W., A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series. National Bureau of Economic Research, Vol. 14, No. 1, (1996), 11-30. doi: 10.3386/w6607
3. Lemke, C. and Gabrys, B., Meta-learning for time series forecasting and forecast combination. Neurocomputing, 73(10-12), (2010), 2006-2016. doi: 10.1016/j.neucom.2009.09.020
4. Ahmadia, E., Abooiea, M. H., Jasemib, M., and Zare Mehrjardi, Y., A Nonlinear Autoregressive Model with Exogenous Variables Neural Network for Stock Market Timing: The Candlestick Technical Analysis. International Journal of Engineering. Transactions C: Aspects, Vol. 29, No. 12, (2016), 1717-1725. doi: 10.5829/idosi.ije.2016.29.12c.10
5. Patel, J., Shah, S., Thakkar, P., and Kotecha, K., Predicting stock market index using fusion of machine learning techniques. Expert Systems with Applications, Vol. 42, No. 4, (2015), 2162-2172. doi: 10.1016/j.eswa.2014.10.031
6. Ahmed, N. K., Atiya, A. F., Gayar, N. E., and El-Shishiny, H., An Empirical Comparison of Machine Learning Models for Time Series Forecasting. Econometric Reviews, Vol. 29, No. 5-6, (2010), 594-621. doi: 10.1080/07474938.2010.481556
7. Palit, A. K. and Popovic, D., Computational Intelligence in Time Series Forecasting: Theory and Engineering Applications. Springer, (2005).
8. Neshat, N., An Approach of Artificial Neural Networks Modeling Based on Fuzzy Regression for Forecasting Purposes. International Journal of Engineering. Transactions B: Applications, Vol. 28, No. 11, (2015), 1651-1655. doi: 10.5829/idosi.ije.2015.28.11b.13
9. Werbos, P. J., Generalization of backpropagation with application to a recurrent gas market model. Neural Networks, Vol. 1, No. 4, (1988), 339-356. doi: 10.1016/0893-6080(88)90007-X
10. Lu, C., Lee, T., and Chiu, C., Financial time series forecasting using independent component analysis and support vector regression. Decision Support Systems, Vol. 47, No. 2, (2009), 115-125. doi: 10.1016/j.dss.2009.02.001
11. Indera, N. I., Yassin, I. M., Zabidi, A., and Rizman, Z. I., Non-linear autoregressive with exogeneous input (narx) Bitcoin price prediction model using pso-optimized parameters and moving average technical indicators. Journal of Fundamental and Applied Sciences, Vol. 9, No. 3, (2017), 791-808. doi: 10.4314/jfas.v9i3s.61
12. McNally, S., Roche, J., and Caton, S., Predicting the Price of Bitcoin Using Machine Learning. 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), (2018). doi: 10.1109/PDP2018.2018.00060
13. Chu, J., Nadarajah, S., and Chan, S., Statistical Analysis of the Exchange Rate of Bitcoin. PLoS ONE, Vol. 10, No. 7, (2015), doi: 10.3386/t0090
14. Dyhrberg, A. H., Bitcoin, gold and the dollar – A GARCH volatility analysis. Finance Research Letters, Vol. 16, (2016), 85-92. doi: 10.1016/j.frl.2015.10.008
15. Hencic, A. and Gouriéroux, C. .Noncausal Autoregressive Model in Application to Bitcoin/USD Exchange Rates. Econometrics of Risk, Vol. 583, (2014), 17-40. doi: 10.1007/978-3-319-13449-9_2
16. Ho, S. L., Xie, M., Goh, T. N., A comparative study of neural network and Box-Jenkins ARIMA modeling in time series prediction. Computers & Industrial Engineering, Vol. 42, (2002), 371-375. doi: 10.1016/S0360-8352(02)00036-0
17. Delfin-Vidal, R. and Romero-Meléndez, G., The Fractal Nature of Bitcoin: Evidence from Wavelet Power Spectra. Trends in Mathematical Economics, (2016), 73-98. doi: 10.1007/978-3-319-32543-9_5
18. Kristoufek, L., What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis. PLoS ONE, Vol. 4, No. 10, (2015). doi: 10.1371/journal.pone.0123923
19. Kristoufek, L., Bitcoin meets Google Trends and Wikipedia: Quantifying the relationship between phenomena of the Internet era. Scientific Reports, Vol. 3, (2013), 1-7, doi: 10.1038/srep03415.
1302 M. Khedmati et al. / IJE TRANSACTIONS A: Basics Vol. 33, No. 7, (July 2020) 1293-1303
20. Garcia, D., Tessone, C. J., Mavrodiev, P., and Perony, N., The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy. Journal of the Royal Society Interface, Vol. 11, No. 99, (2014), 1-8. doi: 10.1098/rsif.2014.0623
21. Shah, D. and Zhang, K., Bayesian regression and Bitcoin. 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), (2014), 409-414. doi: 10.1109/ALLERTON.2014.7028484
22. Greaves, A. and Au, B., Using the Bitcoin transaction graph to predict the price of Bitcoin, (2015). http://snap.stanford.edu/class/cs224w-2015/projects_2015/.
23. Madan, I., Saluja, S., and Zhao, A., Automated Bitcoin trading via machine learning algorithms, (2015). http://cs229.stanford.edu/proj2014/.
24. Almeida, J., Tata, S., Moser, A., and Smit, V. Bitcoin prediciton using ANN. Neural Networks, Vol. 7, (2015), 1-12.
25. Sin, E. and Wang, L., Bitcoin price prediction using ensembles of neural networks. 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), (2017), 666-671. doi: 10.1109/FSKD.2017.8393351
26. Radityo, A., Munajat, Q., and Budi, I., Prediction of Bitcoin exchange rate to American dollar using artificial neural network methods. International Conference on Advanced Computer Science and Information Systems (ICACSIS), (2017), 433-438. doi: 10.1109/ICACSIS.2017.8355070
27. Jang, H. and Lee, J., An Empirical study on modeling and prediction of Bitcoin prices with Bayesian neural networks based on blockchain information. IEEE Access, Vol. 6, (2017), 5427-5437. doi: 10.1109/ACCESS.2017.2779181
28. Rahimi, Z. H., Khashei, M., A least squares-based parallel hybridization of statistical and intelligent models for time series forecasting. Computers & Industrial Engineering, (2018), doi: https://doi.org/10.1016/j.cie.2018.02.023.
29. Lee, K., Ulkuatam, S., Beling, P., and Scherer, W. . Generating synthetic Bitcoin transactions and predicting market price movement via inverse reinforcement learning and agent-based modeling. Journal of Artificial Societies and Social Simulation, Vol. 21, No. 3, (2018), 1-5. doi: 10.18564/jasss.3733
30. Matta, M., Lunesu, I., and Marchesi, M., Bitcoin Spread Prediction Using Social and Web Search Media. UMAP Workshops, (2015).
31. Georgoula, I., Pournarakis, D., Bilanakos, C., Sotiropoulos, D., and Giaglis, G. M., Using Time-Series and Sentiment Analysis to Detect the Determinants of Bitcoin Prices. MCIS 2015 Proceedings, Vol. 20, (2015). doi: 10.2139/ssrn.2607167
32. www.investing.com/crypto/bitcoin/historical-data. (n.d.).
33. Box, P. and Jenkins, G., Time series analysis: forecasting and control. Wiley, (1976).
34. Shi, J., Guo, J., and Zheng, S. . Evaluation of hybrid forecasting approaches for wind speed and power generation time series. Renewable and Sustainable Energy Reviews, Vol. 16, No. 5, (2012), 3471-3480. doi: 10.1016/j.rser.2012.02.044
35. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y., Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics, Vol. 54, No. 1-3, (1992), 159-178.
36. Mann, H. B. , Non-parametric tests against trend. Econometrics, Vol. 13, (1945), 163-171. doi: 10.2307/1907187
37. Gilbert, R. O., Statistical methods for environmental pollution monitoring. John Wiley & Sons, (1987).
38. Kendall, M. G., Rank correlation methods, 4th Edition, Charles Griffin, London, (1975).
39. Breusch, T. S. and Pagan, A. R., A simple test for heteroskedasticity and random coefficient variation. Econometrica, Vol. 47, No. 5, (1979), 1287-1294. doi: 10.2307/1911963
40. Woschnagg, E. and Cipan, J., Evaluating forecast accuracy. UK Ökonometrische prognose, department of economics, university of Vienna, (2004). http://homepage.univie.ac.at/ robert.kunst/procip.pdf.
41. Ankenman, B., Nelson, B. L., and Staum, J., Stochastic Kriging for simulation metamodeling. Operations research, Vol. 58, No. 2, (2010), 371-382. doi: 10.1109/WSC.2008.4736089
42. Kleijnen, J. P., Kriging metamodeling in simulation: A review. European Journal of Operational Research, Vol. 192, No. 3, (2009), 707-716. doi: 10.1016/j.ejor.2007.10.013
43. Journel, A. G., Fundamentals of geostatistics in five lessons. American Geophysical Union, Washington, D.C. , (1989).
44. Cellura, M., Cirrincione, G., Marvuglia, A., and Miraoui, A., Wind speed spatial estimation for energy planning in Sicily: A neural Kriging application. Renewable Energy, Vol. 33, No. 6, (2008), 1251-1266. doi: 10.1016/j.renene.2007.08.012
45. Liu, H., Shi, J., and Erdem, E., Prediction of wind speed time series using modified Taylor Kriging method. Energy, Vol. 35, No. 12, (2010), 4870-4879. doi: 10.1016/j.energy.2010.09.001
46. Azizi, M. J., Seifi, F., Moghadam, S., A robust simulation optimization algorithm using Kriging and particle swarm optimization: Application to surgery room optimization. Communications in Statistics-Simulation and Computation, (2019), doi: 10.1080/03610918.2019.1593452
47. Couckuyt, I. Dhaene, T. Demeester, P., ooDACE Toolbox: A Flexible Object-Oriented Kriging Implementation. Journal of Machine Learning Research, Vol. 15, (2014), 3183-3186.
48. Kolmogorov, A., Interpolation und Extrapolation von stationären zufälligen Folgen. Izv. Akad. Nauk SSSR Ser. Mat., Vol. 5, No. 1, (1941), 3-14.
49. Lauritzen, S. L., Time Series Analysis in 1880: A Discussion of Contributions Made by T.N. Thiele. International Statistical Institute (ISI), Vol. 49, No. 3, (1981), 319-331. doi: 10.2307/1402616
50. Rasmussen, C. E. and Williams, C. K. I., Gaussian Processes in Machine Learning. MIT press, (2006).
51. Efron, B., Large-Scale Inference Empirical Bayes Methods for Estimation, Testing, and Prediction. Vol. 1, Cambridge University Press, (2012).
52. Brahim-Belhouari, S., and Bermak, A., Gaussian process for nonstationary time series prediction. Computational Statistics & Data Analysis, Vol. 47, No. 4, (2004), 705-712. doi: 10.1016/j.csda.2004.02.006
53. Kane, M. J., Price, N., Scotch, M., and Rabinowitz, P. . Comparison of ARIMA and Random Forest time series models for prediction of avian influenza H5N1 outbreaks. BMC Bioinformatics, (2014), Vol. 15:276, doi: 10.1186/1471-2105-15-276
54. Kaastra, I. and Boyd, M., Designing a neural network for forecasting financial and economic time series. Neurocomputing, Vol. 10, No. 3, (1996), 215-236.
55. Azoff, E. M., Neural Network Time Series Forecasting of Financial Markets. New York: John Wiley & Sons, (1994).
56. Zhang, G. P., Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, Vol. 50, (2003), 159-175. doi: 10.1016/S0925-2312(01)00702-0
57. Khashei, M. and Bijari, M., An artificial neural network (p, d, q) model for time series forecasting. Expert Systems with Applications, Vol. 37, No. 1, (2010), 479-489. doi: 10.1016/j.eswa.2009.05.044