Cryptocurrency Price Prediction with Neural Networks of LSTM and Bayesian Optimization
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RESEARCH ARTICLE European Journal of Business and Management Research www.ejbmr.org Cryptocurrency Price Prediction with Neural Networks of LSTM and Bayesian Optimization Ehsan Sadeghi Pour, Hossein Jafari, Ali Lashgari, Elaheh Rabiee, and Amin Ahmadisharaf ABSTRACT In this paper we present a price prediction for Bitcoin prices. The Submitted : February 07, 2022 methodology used is a hybrid artificial neural network model of Long Short- Term Memory and Bayesian Optimization. This is a complex model with a Published : March 07, 2022 high prediction power, which to our knowledge has not been applied to ISSN: 2507-1076 prediction of cryptocurrency prices to date. Following Charandabi and Kamyar (2021), we elaborate on previous methods used for prediction of DOI: 10.24018/ejbmr.2022.7.2.1307 cryptocurrency prices and build on their methodology. We conclude with detailed graphs and tables of optimization results. E. S. Pour Department of Electrical and Computer Keywords: Bayesian optimization, artificial neural networks, cryptocurrency Engineering, Islamic Azad University, price prediction, long short-term memory. Kashan, Iran (e-mail: Ehsan61.ai@gmail.com) H. Jafari Master of Accounting, Allameh Amini Institute of Higher Education, Mazandaran, Iran. (email: hossein.jafari2008@gmail.com) A. Lashgari* Department of Economics, Kansas State University, Manhattan, KS, USA. (e-mail: alilashgari@ksu.edu) E. Rabiee Department of Economics, Kansas State University, Manhattan, KS, USA. (e-mail: elahehrabiee@ksu.edu) A. Ahmadisharaf Kansas State University, Manhattan, KS, USA. (e-mail: ahmadish@ksu.edu) *Corresponding Author combination with one another to improve accuracy and I. INTRODUCTION predictive power. Charandabi and Kamyar (2021B) present a survey on the literature on applications of artificial neural The world has gone through many changes since 2009. Just networks to cryptocurrency price prediction. Based on their over the last 13 years Instagram was founded, Steve Jobs reports, there have been a number of hybrid and singular passed away, a whole pandemic started, and so on. But an artificial neural network models implemented so far; extremely important event that happened in 2009 hand has however, there are still numerous gaps to be filled in the been changing the world since is the launch of Bitcoin. While literature. the cryptocurrency was conceptualized back in 1990’s, it was This paper serves to fill the literature by providing a model not relevant to the public until years after Bitcoin was first of Neural Networks of LSTM and Bayesian Optimization. In implemented. The rate of increase in popularity is so high that Section II, we review related literature; in Section III, we Bitcoins which barely sufficed to by a pizza in 2010, costed discuss the data process, in Section IV we go through as high as $68000 in 2021. optimization details, and in section V we conclude. Financial analysts attribute the popularity of Bitcoin to its decentralization, secure blockchain system, and control over value. Charandabi and Kamyar (2021A) presents a thorough II. LITERATURE REVIEW survey of the history, foundation, and relevance of Bitcoin. In the same paper, they argue on the importance and relevance “Artificial neural networks (ANNs) are biologically of artificial neural networks to predict prices of inspired computational networks. Multilayer perceptrons cryptocurrency. Artificial neural networks may have a high (MLPs), the ANNs most commonly used for a wide variety predictive power and can be pertained to cryptocurrency price of problems, are based on a supervised procedure and data in any time horizon. comprise three layers: input, hidden, and output.” (Park & Artificial neural network models can be used in Lek, 2016) In this context, artificial neural networks may be DOI: http://dx.doi.org/10.24018/ejbmr.2022.7.2.1307 Vol 7 | Issue 2 | March 2022 20
RESEARCH ARTICLE European Journal of Business and Management Research www.ejbmr.org powerful tools to predict growing or volatile numerical view the data aspect of this research paper as a novel work in values. the literature. All exchange rates are with respect to United Within the financial literature, artificial neural networks States Dollars. have been applied to prediction of stocks market indices since decades ago. Singular networks often have a lower predictive power than hybrid models, though they take shorter to IV. OPTIMIZATION compute. (Ghashami et al., 2021) Here we present a series of The baseline treatment is prediction of Bitcoin prices with price prediction for Bitcoin prices. The methodology used is Neural Networks of LSTM and Bayesian Optimization. The a hybrid artificial neural network model of Long Short-Term value of optimal delays is set to 1.30, and the value of optimal Memory and Bayesian Optimization. This complex model training percentage (division of data to training and testing) has a high predictive power over prediction of numerical is set to 0.8 (Nejatian, 2022). Furthermore, to optimize speed, values. To our knowledge, it has not been applied to the the optimal code execution environment is the CPU. The context of prediction of cryptocurrency prices to date optimal drop out value is 0.5. These values are endogenous to “Long Short-Term Memory (LSTM) is a specific recurrent the model and remain constant across the treatments. neural network (RNN) architecture that was designed to Some general deep learning parameters are exogenously model temporal sequences and their long-range dependencies varied across treatments. In the baseline, the maximum more accurately than conventional RNNs.” (Sak et al., 2014) number of training Epochs in deep learning algorithms As described in the survey of Charandabi & Kamyar (2021B), (maxEpoch) is set equal to 400. Following standard LSTM is frequently a candidate for hybrid artificial neural cryptocurrency optimization literature (Charandabi & network models. Another optimization method, Bayesian Kamyar, 2021C) we exogenously set it to 200 in the treatment Optimization, is a sequential design strategy for global run. Additionally, in the baseline, the minimum batch size of optimization of black-box (unknown internal structure) training Epochs in deep learning algorithms is set equal to 32. functions (Mockus 2012). The novel hybrid structure of Following standard cryptocurrency optimization literature LSTM and Bayesian Optimization has been tested on stock (Charandabi & Kamyar, 2021C) we exogenously set it to 16 market indices (Huang et al., 2018) and showed a high in the treatment run. predictive power, therefore, we view it as suitable for We start reporting results by the baseline of Bitcoin prices prediction of cryptocurrency indicators. (weekly from January 2020 through January 2022), As elaborated on in Charandabi & Kamyar (2021C), the maximum training Epoch number of 400, and batch size of high volatility of cryptocurrency prices roots from maximal training Epochs in deep learning algorithms of 32. Fig. 1 trading, that stems from uncertainty. Decision-making under depicts the input data, reporting the values for mean and under unforeseen events has been the focus of research in the standard deviation as well. The algorithm normalizes input last few decades (Asadi et al., 2022). More recently, data prior to running, in order for the base numbers to be (Dehghani Filabadi 2019), Filabadi (2022) proposed general feasible for computational concerns. Fig. 2 depicts the mathematical models for addressing uncertainties in normalized input data, reporting the values for mean and environments where data is sensitive to prediction errors. standard deviation as well. In the green and blue lines, Fig. 3 This approach was further extended for other applications depicts the minimum observed objective and estimated such as energy management (Filabadi & Azad, 2020), minimum objective, respectively. network management (Filabadi & Bagheri, 2021), and inventory and healthcare (Filabadi & Mahmoudzadeh, 2022). III. DATA We extracted data from Yahoo! Finance, a major resource for daily data on financial indices and cryptocurrency prices. Ghashami et al. (2021) elaborates on data gathering for financial indicators for the purposes of time-series prediction through artificial neural network methodology. We follow the same system for optimization of data points among the daily values for Open, High, Low, Close, and Adj. Close. Cryptocurrency data is extremely volatile by nature. There’s a body of literature dedicated to prediction of volatility of cryptocurrency price data, as explained thoroughly in the survey paper Charandabi & Kamyar (2021C). In order to avoid running into problems and Fig. 1. Input data of first treatment. retrieving weak predictions, we use weekly data, and expand the time horizon instead. The employed data runs from January 10, 2020, to January 10, 2022, on a weekly basis. Most of the literature on prediction of cryptocurrency prices employ data from a short time horizon, as explained in the survey paper Charandabi & Kamyar (2021B). Therefore, we DOI: http://dx.doi.org/10.24018/ejbmr.2022.7.2.1307 Vol 7 | Issue 2 | March 2022 21
RESEARCH ARTICLE European Journal of Business and Management Research www.ejbmr.org Fig. 2. Normalized input data of first treatment. Fig. 5. Error mean evaluation. Fig. 3. Minimum observed objective and estimated minimum objective values. Fig. 6. Error histogram. Fig. 4-7 depict technical aspects of training data. Fig. 4 shows the output evaluation and reports the rank correlation number, which is significantly high. Fig. 5 shows the error evaluation and reports the MSE (Mean Squared Error), RMSE (Rooted Mean Square Error), and NRMSE (Normalized Rooted Mean Square Error). Figure 6 shows the error histogram, reporting Error Mean and Error Standard Deviation numbers. Fig. 7 shows the Regression Graph Evaluation of train data, reporting the R-squared value, that is highly significant. Fig. 7. Regression graph evaluation. The output results had Maximum Objective Evaluations of 60 reached. Total time elapsed was 849.8 seconds, with a total function evaluation count of 60 and a total objective function evaluation time of 766.6 seconds. Observed objective function value was 0.07662, with an estimated objective function value of 0.15971 and a function evaluation time of 7.8227. Also, estimated objective function value was 0.14654 and estimated function evaluation time was 6.7355. Fig. 8- 10 represent technical aspects of the test data. Fig. 8 depicts Fig. 4. Output evaluation. output evaluation, and reports rank correlation value. Fig. 9 shows the error evaluation and reports the MSE (Mean DOI: http://dx.doi.org/10.24018/ejbmr.2022.7.2.1307 Vol 7 | Issue 2 | March 2022 22
RESEARCH ARTICLE European Journal of Business and Management Research www.ejbmr.org Squared Error), RMSE (Rooted Mean Square Error), and MSE (Mean Squared Error), RMSE (Rooted Mean Square NRMSE (Normalized Rooted Mean Square Error). Fig. 10 Error), and NRMSE (Normalized Rooted Mean Square Error) shows the error histogram, reporting Error Mean and Error of all data. Fig. 12 depicts regression evaluation of all data, Standard Deviation numbers. reporting the R-squared value. Fig. 8. Output evaluation of test data. Fig. 11. Error mean evaluation. Fig. 9. Error mean evaluation of test data. Fig. 12. Regression graph evaluation. Table I shows technical details of the best observed feasible point (above) and the best estimated feasible point (below), according to the models. All points are on the first layer. TABLE I: BEST FEASIBLE POINTS LSTM Initial Layer 2 Number of Units Layer Learn Rate Reg. 68 2 0.016 0.00475 71 2 0.021 0.00798 The treatment run employed the same methodology and data, with the exception of the maximum number of training Epochs in deep learning algorithms (maxEpoch) set equal to 200, and the minimum batch size of training Epochs in deep Fig. 10. Error histogram of test data. learning algorithms set equal to 16. In the green and blue lines, Fig. 13 depicts the minimum observed objective and Fig. 11 and 12 show technical details of all (i.e., train and estimated minimum objective, respectively. test) data. Fig. 11 depicts the error evaluation and reports the DOI: http://dx.doi.org/10.24018/ejbmr.2022.7.2.1307 Vol 7 | Issue 2 | March 2022 23
RESEARCH ARTICLE European Journal of Business and Management Research www.ejbmr.org Fig. 13. Minimum observed objective and estimated minimum objective values. Fig. 16. Error histogram. Fig. 14-17 depict technical aspects of training data. Fig. 14 shows the output evaluation and reports the rank correlation number, which is significantly high. Fig. 15 shows the error evaluation and reports the MSE (Mean Squared Error), RMSE (Rooted Mean Square Error), and NRMSE (Normalized Rooted Mean Square Error). Fig. 16 shows the error histogram, reporting Error Mean and Error Standard Deviation numbers. Fig. 17 shows the Regression Graph Evaluation of train data, reporting the R-squared value, that is highly significant. Fig. 17. Regression graph evaluation. The output results had Maximum Objective Evaluations of 60 reached. Total time elapsed was 849.8 seconds, with a total function evaluation count of 60 and a total objective function evaluation time of 1271.6 seconds. Observed objective function value was 0.08878, with an estimated objective function value of 0.13354 and a function evaluation time of 18.863. Also, estimated objective function value was 0.071925 and estimated function evaluation time was 9.4717. Fig. 14. Output evaluation. Fig. 18-20 represent technical aspects of the test data. Fig. 18 depicts output evaluation, and reports rank correlation value. Fig. 19 shows the error evaluation and reports the MSE (Mean Squared Error), RMSE (Rooted Mean Square Error), and NRMSE (Normalized Rooted Mean Square Error). Fig. 20 shows the error histogram, reporting Error Mean and Error Standard Deviation numbers. Fig. 21 and 22 show technical details of all (i.e., train and test) data. Fig. 21 depicts the error evaluation and reports the MSE (Mean Squared Error), RMSE (Rooted Mean Square Error), and NRMSE (Normalized Rooted Mean Square Error) of all data. Fig. 22 depicts regression evaluation of all data, reporting the R-squared value. Table II shows technical details of the best observed feasible point (above) and the best estimated feasible point (below), according to the models. Fig. 15. Error mean evaluation. DOI: http://dx.doi.org/10.24018/ejbmr.2022.7.2.1307 Vol 7 | Issue 2 | March 2022 24
RESEARCH ARTICLE European Journal of Business and Management Research www.ejbmr.org TABLE II: BEST FEASIBLE POINTS Number of Number of LSTM Initial Layer 2 Layer Units Layer Learn Rate Reg. 3 61 1 0.021 0.00881 1 54 2 0.012 0.00889 While the 200-16 model provides less noise in the resulting data and filters volatilities, the 400-32 model yields a shorter elapsed time and higher accuracy factors. Fig. 21. Error mean evaluation. Fig. 18. Output evaluation of test data. Fig. 22. Regression graph evaluation. V. CONCLUSION In this paper, we applied a novel algorithm for prediction of time-series data (through hybrid artificial neural networks of Long Short-Term Memory and Bayesian Optimization) to prediction of Bitcoin data. We ran two treatments of data and training variables using Bitcoin prices (weekly from January 2020 through January 2022): maximum training Epoch Fig. 19. Error mean evaluation of test data. number of 400 and 200, and batch size of training Epochs in deep learning algorithms of 32 and 16. Results were reported graphically and in tables, and optimal solutions were comparatively shown. There exist many possible extensions to this paper. One may run the same algorithm with different data to compare consistency of external validity to other contexts. Other bitcoin prices (e.g., Ethereum) may be good candidates. Alternatively, within the financial data realm, stock market indices could be tested with the same algorithm. Furthermore, other hybrid models such as a hybrid of the current model with a GA-ANFIS artificial neural network algorithm a la Ghashami & Kamyar (2021) could be implemented to increase the accuracy. In light of the current impact and relevance of cryptocurrency prices, it’s essential that further models be tested. Fig. 20. Error histogram of test data. DOI: http://dx.doi.org/10.24018/ejbmr.2022.7.2.1307 Vol 7 | Issue 2 | March 2022 25
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