Measurement of Bitcoin Daily and Monthly Price Prediction Error Using Grey Model, Back Propagation Artificial Neural Network and Integrated model of Grey Neural Network

محورهای موضوعی : Numerical Methods in Mathematical Finance

Mahdi Madanchi Zaj ¹ , Mohammad Ebrahim Samavi ² , Emad Koosha ³

1 - Department of Financial Management, Electronic Campus, Islamic Azad University Tehran, Iran
2 - Department of Finance, College of Management and Economics, Financial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3 - Department of Finance, Financial Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

تاریخ دریافت : 1399/04/25 تاریخ پذیرش : 1399/08/18 تاریخ انتشار : 1401/04/10

کلید واژه: Grey-Neural Network, Back Propagation Artificial Neural Network, Grey Model, Bitcoin, block chain,

چکیده مقاله :

One of the recent financial technologies is Block chain-based currency known as Cryptocurrency that these days because of their unique features has become quite popular. The first known Cryptocurrency in the world is Bitcoin, and since the cryptocurrencies market is a contemporary one, Bitcoin is currently considered as the pioneer of this market. Since the value of the previous Bitcoin prices data have a non-linear behaviour, this study aims at predicting Bitcoin price using Grey model, Back Propagation Artificial Neural Network and Integrated Model of Grey Neural Network. Then, the prediction’s accuracy of these methods will be measured using MAPE and RMSE indices and also Bitcoin price data for a five-year period (2014-2018). The results had indicated that wen estimating Bitcoin daily prices, Back Propagation Artificial Neural Network model has the lowest absolute error rate (5.6%) compared to the Grey model and the integrated model. Additionally, for the monthly prediction of Bitcoin price, the integrated model, with the lowest absolute error rate (9%), has a better performance than the two other models.

منابع و مأخذ:

[1] Alijani, M., Banimahi, B., Madanchi Zaj, M., Study and Research on the Six-Year Process of Bitcoin Price and Return, Advances in mathematical finance and applications, 2019, 4(1), P.45-54. Doi: 10.22034/AMFA.2019.577434.1126

[2] Da Silva Filho, AC, Diniz Maganini, N., de Almeida, E.F., Multifractal analysis of Bitcoin market, 2018, Physica conference, Doi: 10.1016/j.physa.2018.08.076

[3] Atsalakis, G.S., Valavanis, K.P., Surveying stock market forecasting techniques – Part II: Soft computing methods. Expert Systems with Applications, 2009, 36(3), P. 5932-5941. Doi: 10.1016/j.eswa.2009.02.043

[4] Balcilar, M., Bouri, E., Gupta, R., Roubaud, D., Can Volume Predict Bitcoin Returns and Volatility? A Quantiles-Based Approach. Economic Modelling, 2017,  64(2), P. 74-81, Doi: 10.1016/j.econmod.2017.03.019

[5] Baur, D.G., Hong, K., Lee, A.D., Bitcoin: Medium of exchange or speculative assets? Journal of International Financial Markets, Institutions and Money, 2018, 54, P. 177-189. Doi: 10.1016/j.intfin.2017.12.004

[6] Bouri, E. Jalkh, N., Molnár P., Roubaud D, Bitcoin for energy commodities before and after the December 2013 crash: diversifier, hedge or safe haven? Applied Economics, 2017, 49, P.5063-5073.Doi: 10.1080/00036846.2017.1299102

[7] Bouri, E., Gupta, R., Tiwari, A.K., Doubaud, D, Does Bitcoin hedge global uncertainty? Evidence from wavelet-based quantile-in-quantile regressions, Finance Research Letters, 2017, 23, P. 87-95.Doi: 10.1016/j.frl.2017.02.009

[8] Bouri, E., Molnár, P., Azzi, G., Roubaud, D., Hagfors, L.I, On the hedge and safe haven properties of Bitcoin: is it really more than a diversifier, Finance Research Letters, 2017, 20, P.192–198. Doi:  10.1016/j.frl.2016.09.025

[9] Bradbury, D, The problem with Bitcoin. Computer Fraud & Security, 2013, 11, P. 15–38.Doi: 10.1016/S1361-3723(13)70101-5

[10] Cheah, E. T., Fry, J, Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Economics Letters, 2015,130, P. 32-36. Doi: 10.1016/j.econlet.2015.02.029

[11] Chen, S-J., Huang, C-I, The Necessary and Sufficient condition for GM (1,1) Grey prediction Model, Applied Mathematics and Computation, 2013,  219(11),  P. 6152-6162. Doi: 0.1016/j.amc.2012.12.015

[12] Burniske, C., Tatar, J., Crypto Assets: the innovative investor's guide to Bitcoin and beyond, McGraw-Hill Education, 2017, ISBN-13: 978-1260026672.

[13] Chuen, D. L. K., Handbook of digital currency: Bitcoin, innovation, financial instruments, and big data, Academic Press, 2015, 2(1), P. 112-131.

[14] Dash, R., Dash, P.K., A hybrid stock trading framework integrating technical analysis with machine learning techniques, The Journal of Finance and Data Science (JFDS), 2016, 2, P.42-57. Doi:10.1016/j.jfds.2016.03.002

[15] Vidal-Tomas, D., Ibanez, A., Semi-strong efficiency of Bitcoin, Finance Research Letters, 2018, 14, P. 32-45. Doi: 10.1016/j.frl.2018.03.013

[16] De La Horra, G., de la Fuente and J. Perote, the drivers of Bitcoin demand: A short and long-run analysis, International Review of Financial Analysis, 2019, 62, P. 21-34. Doi:10.1016/j.irfa.2019.01.006

[17] Demir, E., Gozgor, G., Lau, C.K.M., Vigne, S.A., Does economic policy uncertainty predict the Bitcoin returns? An empirical investigation. Finance Research, Letters, 2018, 26, P.145-149.Doi: 10.1016/j.frl.2018.01.005

[18] Julong, D., Introduction to Grey System Theory. The Journal of Grey system,1989, 1(3), P.1 -24.

[19] Dyhrberg A.H., Foley S., Svec J., How investible is Bitcoin? Analyzing the liquidity and transaction costs of Bitcoin markets, Economics Letters, 2018, 32, P. 123-151. Doi:10.1016/j.econlet.2018.07.032

[20] Elwell, C. K., Murphy, M. M., and Seitzinger, M. V., Bitcoin: Questions, Answers, and Analysis of Legal Issues, US Congressional Research Service, Washington, 20 December 2013.

[21] European Central Bank, Virtual currency schemes–a further analysis, European Central Bank, 2015, retrieved from: https://www.ecb.europa.eu/pub/pdf/other/virtualcurrencyschemesen.pdf

[22] European Central Bank, Virtual Currency Schemes. Technical Report, October, 2012. Available at https://www.ecb.europa.eu/pub/pdf/other/ virtualcurrencyschemes201210en.pdf

[23] Atsalakis, G.S., Atsalaki, I.G., Pasiouras, F., Zopounidis, C., Bitcoin price forecasting with neuro-fuzzy techniques, European Journal of Operational Research, 2019, 276(2), P.770-780. Doi:10.1016/j.ejor.2019.01.040

[24] Georgoula, I., Pournarakis, D., Bilanakos, C., Sotiropoulos, D., Giaglis G., Using Time-Series and Sentiment Analysis to Detect the Determinants of Bitcoin Prices, 2015, 25(2), P.110-122. Doi: 10.2139/ssrn.2607167

[25] Glaser, F., Bitcoin-asset or currency? revealing users' hidden intentions, ECIS, 2014, 12(3), P.127-141. Available in: ssrn.com/abstract=2425247

[26] Guo, J., Chow, A., Virtual money systems: a phenomenal analysis, Paper presented at the 10th IEEE Conference,2008. Doi:10.1109/CECandEEE.2008.91

[27] Guresen, E., Kayakutlu, G., Daim, T. U., Using artificial neural network models in stock market index prediction Expert Systems with Applications, 2001, 38(8), P.10389–10397. Doi: 10.1016/j.eswa.2011.02.068

[28] Halaburda, H., Sarvary, M., Beyond Bitcoin, The Economics of Digital Currencies, 2016. ISBN 978-1-137-50642-9

[29] Harvey, C.R., Travers, K.E., Costa, M.J, forecasting emerging markets returns using neural networks. Emerging Markets Quarterly, 2000, 4, P. 43–54. ssrn.com/abstract=2214219

[30] Hatefi Majoomard, M, Jalali, U, Rahimi Ghasem Abadi, M, Spectacular Bubbles in the Bitcoin Digital Currency Market, Quarterly Journal of Financial Knowledge of Securities Analysis, 2018, 40(3), P. 189-204. (In Persian). Available at: jfksa.srbiau.ac.ir/article_13614.html

[31] He, D., Habermeier, K. F., Leckow, R. B., Haksar, V., Almeida, Y., Kashima, M., Yepes, C. V., Virtual Currencies and Beyond: Initial Considerations (No. 16/3). International Monetary Fund, 2016. ISBN/ISSN:9781498363273

[32] Islamic Republic of Iran Central Bank, The Document of Rules and Regulations of Cryptocurrencies, 2019, Issues 01.

[33] Wang, J.S., Ning, C-X., Cui, W-H., Time Series Prediction of Bank Cash Flow Based on Grey Neural Network Algorithm. International Conference on Estimation, Detection and Information Fusion, 2015, 12(1), P. 27- 39. Doi:10.1109/ICEDIF.2015.7280205

[34] Su, J., Zhou, J., The Use of Grey Verhulst Model in the Prediction of Operating Activities Cash Flow. Fourth International Conference on Business Intelligence and Financial Engineering, 2011, 14, P. 19-32.Doi: 10.1109/BIFE.2011.147

[35] Madan, I., Saluja, S., Zhao, A., Automated Bitcoin trading via machine learning algorithms, 2018, 5(1), P.16-32. Doi: 10.1155/2018/8983590

[36] Malek, A.M., Dabaghi, A., Fundamentals of the Theory of Grey Systems, Terhmeh Publications, 2011, (in Persian).

[37] Nadarajah, S., Chu, J., On the inefficiency of Bitcoin, Economics Letters, Elsevier, 2017, 150(3), P. 6-19.Doi: 10.1016/j.econlet.2016.09.019

[38] Xie, N-M., Liu, S-F., Discrete grey forecasting model and its optimization, Applied Mathematical Modelling, 2009, 33, P.1173–1186. Doi: 10.1016/j.apm.2008.01.011

[39] Nakamoto, S., Bitcoin: A Peer-to-Peer Electronic Cash System, Bitcoin.org, 2008, Available via: http://Bitcoin.org/Bitcoin.pdf.

[40] Nasr, N., Farhadi Sartangi, M., Madahi, Z., A Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index, 2019, 4(1), P. 15-30. Doi: 10.22034/AMFA.2019.583911.1172

[41] Polasik, M., Piotrowska, A.I., Wisniewski, T.P., Kotkowski, R., Lightfoot, G., Price Fluctuations and the Use of Bitcoin: An Empirical Inquiry. International Journal Electronic Commerce, 2015, 20, P.9-49.Doi: 10.2139/ssrn.2516754

[42] Rogojanu, A., Badea, L., the issue of" true" money in front of the Bitcoin's offensive, Theoretical and Applied Economics, 2015, 22(2), P.77-90. Doi: ideas.repec.org/a/agr/journl/vxxiiy2015i2(603). p77-90.html

[43] Seyyed Hosseimi, M., Doayi, M., Bitcoin, The First Cryptocurrency, Bourse Monthly Journal, 2014, 114, P. 13-19 (In persian).

[44] Shah, D., Zhang, K., Bayesian regression and Bitcoin, 2014, 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton). Doi:10.1109/ALLERTON.2014.7028484

[45] Sheng-Chai, C.,  Hung-Pin, C, ; Chun-Hao, C., A forecasting approach for stock index future using grey theory and neural networks,1999, 18(1), P.28-36.

[46] Soleymanipour, M., Jurisprudential Investigation into Virtual Money, Islamic Finance Researches, 2017, 6(2), P. 27-45 (In Persian).

[47] Tafaghodi Asrari, M., History of Money and Its Evolution, Historical Studies, 2017, 54(3), P.19- 34 (In Persian).

[48] Urquhart, A., The inefficiency of Bitcoin, Economics Letters, 2016, 148(3), P.80–92.
Doi: 10.1016/J.ECONLET.2016.09.019

[49] Yermack, D., Is Bitcoin a real currency? An economic appraisal, National Bureau of Economic Research, The Handbook of Digital Currency, 2014, 37(1), P. 31-44. DOI: 10.1016/B978-0-12-802117-0.00002-3

[50] Zhu, Y., Dickinson, D., Li, J., Analysis on the influence factors of Bitcoins price based on VEC model. Financial Innovation, 2017, 3(3), P. 28-33. Doi: 10.1186/s40854-017-0054-0

[51] Gholami Jamkarani, R., Mokhtari Kajori, D., Effect of Conservative Reporting on Investors' Opinion Divergence at the Time of Earnings Announcement, Advances in mathematical finance and applications, 2018, 3(2), P. 81-95. Doi: 10.22034/AMFA.2018.540833