On Forecasting Cryptocurrency Prices: A Comparison of Machine Learning, Deep Learning, and Ensembles
Abstract
:1. Introduction
2. Materials and Methods
2.1. Predictive Models
 Auto Regressive Integrated Moving Average (ARIMA). This is a generalisation of the simpler ARMA model (auto regressive moving average). The traditional threestep process of constructing ARIMA models by [13], includes model identification, parameter estimation, and finally, the diagnosis of the simulation and its verification. Essentially, a prediction for a ${y}_{{t}_{target}}$ value is the linear combination of the ${y}_{{t}_{i}}$ values up to the ${t}_{target}$ timestamp and the prediction errors made for the same ${y}_{{x}_{{t}_{i}}}$ values. Examples of ARIMA usage include forecasting for air transport demand [23,24], longterm earning prediction [25], and nextday electricity price prediction [26]. ARIMA has effectively predicted BTC prices in [6,14,27].
 kNearest Neighbor (kNN). Originally suited for classification tasks, kNN is a nonparametric model that has been successfully extended and employed for regression tasks in time series analysis. To predict ${y}_{{t}_{target}}$, the kNN calculates the k mostsimilar ${x}_{{t}_{i}}$ values to ${x}_{{t}_{target}}$. Then, prediction of ${y}_{target}$ is the weighted average of the k${y}_{{t}_{i}}$ values. The kNN model has been used in financial forecasting [28], electric market price prediction [29], and in the prediction of Bitcoin [30].
 Support Vector Regression (SVR). Built on support vector machines for classification, SVR enables both linear and nonlinear regression. Similarly to kNN, SVR is a nonparametric methodology introduced by [31]. SVR aims to maximise generalisation performance when designing regression functions [32]. SVR was applied to a variety of time series tasks such as forecasting warranty claims [32], predicting blood glucose levels [33], and for stock predictions in the financial market [34]. Examples of SVR usage in forecasting crypto prices can be found in [20,21].
 Random Forest (RF) Regressor. This is essentially an ensemble of decision trees, each of which is built on a random subset of the training set. RF’s predictions are performed by averaging the predictions of individual trees. The key benefits of RF are its generalisation capability, and minimal sensitivity to hyperparameters [35]. RF has been used in time series tasks for forecasting cyber security incidents [36], for the prediction of methane outbreaks in coal mines usage [37], and for projecting monthly temperature variations [35]. In the prediction of cryptos, RF has been used for BTC forecasting in [20] and BTC, ETH, and XRP in [19].
 Long Short Term Memory (LSTM). This is a type of RNN capable of learning longterm dependencies and, therefore, is suitable for time series analysis [38]. Although LSTMs follow a chainlike structure similar to ordinary RNNs, in an LSTM’s repeating module, four neural layers interact, i.e., two in the input gate, one in the forget gate, and one in the output gate. The input gate adds or updates new information, and the forget gate removes irrelevant information. The output gate ultimately passes updated information to the following LSTM cell. Examples of LSTM usage can be found in shortterm travel speed prediction [39], predicting healthcare trajectories from medical records [40], and forecasting aquifer levels [41]. The model has also been successful for crypto price prediction [7,8,9].
 Gated Recurrent Unit (GRU). Although the GRU model is similar to LSTM, the former improves upon the computational efficiency of the latter because it has fewer external gating signals in the interpolation. Consequently, the related parameters are reduced. GRU has been used in the shortterm prediction for a bikesharing service [42], network traffic predictions [43], and forecasting airborne particle pollution [44]. GRU was found in [10] to forecast the prices of BTC, ETH, and LTC successfully.
 LSTMGRU (HYBRID). This method was proposed by Patel et al. [11] to avail of the advantages of both LSTM and GRU. Their study indicated that this hybrid approach effectively predicted Litecoin and Monero daily prices, for this reason we include it herein. Combinations of LSTM and GRU have been successfully applied to predict water prices [45].
 Temporal Convolution Network (TCN). Presented by Bai, Kolter, and Koltun [46], TCN is a variant of the convolutional neural network architecture, and uses dilated, causal, onedimensional convolutional layers. TCN’s causal convolutions prevent future data from leaking into the input. TCNs have been widely adopted in time series forecasting. For example, TCNs can produce a shortterm prediction of wind power [47], predict justintime design smells [48], and forecast in stock volatility [49]. In addition, TCN was effective at forecasting weekly Ethereum prices [50].
 Temporal Fusion Transformer (TFT). Introduced by [51], the architecture of TFT is built on the vanilla transformer architecture. TFT is one of the most recent deep learning approaches for time series forecasting. Its design incorporates novel components such as gating mechanisms, variable section networks, static covariates, prediction intervals, and temporal processing. TFT has been applied in other time series tasks such as the prediction of pH levels in bodies of water [52], flight demand forecasting [53], and projecting future precipitation levels [54]. To the best of our knowledge, we are the first to employ it for the crypto price prediction.
2.2. Data Collection
 ${t}_{i}$—the timestamp of the day;
 $O{P}_{{t}_{i}}$—the opening price of the cryptocurrency at ${t}_{i}$;
 $H{P}_{{t}_{i}}$—the highest price of the cryptocurrency at ${t}_{i}$;
 $L{P}_{{t}_{i}}$—the lowest price of the cryptocurrency at ${t}_{i}$;
 ${y}_{{t}_{i}}$—the target variable, i.e., the closing price of the cryptocurrency at ${t}_{i}$ (which corresponds to the opening price of the following day, i.e., $O{P}_{{t}_{i+1}}={y}_{{t}_{i}}$).
2.3. Data PreProcessing
2.4. Experimental Methodology
2.5. Evaluation Metrics
3. Results
3.1. Individual Models
3.2. Ensembles
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. The Hyperparameter Values of the Predictive Models
Model  Python Library  Architecture  Hyperparameters Used 

LSTM  TensorFlow  Single Convolutional Layer and a LSTM Layer. 

GRU  TensorFlow  Single GRU Layer and Dense Layer. 

LSTMGRU Hybrid  TensorFlow  Two LSTM Layers and a GRU Layer. 

TCN  TensorFlow  Four Convolutional Layers 

TFT  DARTS 
 
RF  ScikitLearn 
 
SVR  ScikitLearn 
 
kNN  ScikitLearn 
 
ARIMA  StatsModel 

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Name  Release Year  Market Cap ^{1}  24 h Volume ^{1}  Min Price ^{2}  Max Price ^{2}  Mean Price ^{2}  Price SD ^{2} 

Bitcoin (BTC)  2009  393.41  45.67  1914.10  67,525.83  18,621.99  17,623.38 
Etherium (ETH)  2015  192.46  19.31  83.76  4807.98  1021.77  1220.11 
Litecoin (LTC)  2011  3.93  0.53  23.08  387.80  101.41  64.33 
Monero (XMR)  2014  2.71  0.09  29.20  484.00  142.39  90.43 
XRP (XRP)  2012  22.96  0.96  0.14  2.78  0.51  0.36 
Model  RMSE  MAE  MAPE  R2  Train (s)  Inference (ms) 

LSTM  0.02224  0.0173  3.862%  0.735  173.765  1.862 
GRU  0.02285  0.0176  3.939%  0.720  254.520  1.550 
HYBRID  0.02295  0.0177  3.959%  0.717  461.967  2.383 
KNN  0.02332  0.0179  4.003%  0.711  <0.01  0.074 
TCN  0.02334  0.0180  4.021%  0.711  40.475  1.219 
ARIMA  0.02343  0.0180  4.010%  0.708  4.035  0.109 
TFT  0.02353  0.0181  4.062%  0.707  105.913  8.842 
RF  0.02402  0.0184  4.095%  0.697  2.121  0.586 
SVR  0.02452  0.0189  4.240%  0.681  <0.01  0.008 
BTC  ETH  LTC  XMR  XRP  Average  

LSTM  0.0239 (1)  0.030 (1)  0.0189 (1)  0.0236 (1)  0.0148 (1)  0.0222 (1) 
GRU  0.0245 (2)  0.0309 (2)  0.0193 (2)  0.0243 (2)  0.0153 (2)  0.0229 (2) 
HYBRID  0.0246 (3)  0.0309 (3)  0.0195 (3)  0.0244 (3)  0.0154 (3)  0.0230 (3) 
KNN  0.0249 (6)  0.0319 (5)  0.0197(4)  0.0245 (5)  0.0155 (4)  0.0233 (4) 
TCN  0.0250 (7)  0.0319 (4)  0.0198 (5)  0.0245 (6)  0.0156 (5)  0.0233 (5) 
ARIMA  0.0251 (8)  0.0320 (7)  0.0198 (6)  0.0244 (4)  0.0158 (7)  0.0234 (6) 
TFT  0.0249 (5)  0.0319 (6)  0.0199 (7)  0.0250 (7)  0.0159 (8)  0.0235 (7) 
RF  0.0266 (9)  0.0332 (8)  0.0199 (8)  0.0251 (8)  0.0157 (6)  0.0240 (8) 
SVR  0.0248 (4)  0.0342 (9)  0.0207 (9)  0.0268 (9)  0.0160 (9)  0.0245 (9) 
Ensemble  RMSE  MAE  MAPE  R2 

LSTM  0.0222  0.0173  3.86%  0.73 
GRU, LSTM  0.0225  0.0174  3.89%  0.73 
HYBRID, LSTM  0.0225  0.0174  3.89%  0.73 
HYBRID, GRU, LSTM  0.0226  0.0175  3.90%  0.73 
LSTM, KNN  0.0227  0.0175  3.92%  0.73 
GRU, LSTM, KNN  0.0227  0.0176  3.91%  0.72 
GRU, LSTM, TCN  0.0227  0.0176  3.92%  0.72 
LSTM, TCN  0.0227  0.0176  3.93%  0.72 
HYBRID, LSTM, KNN  0.0227  0.0175  3.92%  0.72 
HYBRID, GRU, LSTM, KNN  0.0227  0.0175  3.91%  0.72 
Model  RMSE with Model  RMSE without Model  Difference (%) ^{1} 

LSTM  0.023  0.0233  1.26% 
GRU  0.0231  0.0232  0.57% 
HYBRID  0.0231  0.0232  0.48% 
KNN  0.0232  0.0232  −0.03% 
TCN  0.0232  0.0232  −0.06% 
ARIMA  0.0232  0.0231  −0.2% 
TFT  0.0232  0.0231  −0.21% 
RF  0.0232  0.0231  −0.41% 
SVR  0.0233  0.0231  −0.87% 
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Murray, K.; Rossi, A.; Carraro, D.; Visentin, A. On Forecasting Cryptocurrency Prices: A Comparison of Machine Learning, Deep Learning, and Ensembles. Forecasting 2023, 5, 196209. https://doi.org/10.3390/forecast5010010
Murray K, Rossi A, Carraro D, Visentin A. On Forecasting Cryptocurrency Prices: A Comparison of Machine Learning, Deep Learning, and Ensembles. Forecasting. 2023; 5(1):196209. https://doi.org/10.3390/forecast5010010
Chicago/Turabian StyleMurray, Kate, Andrea Rossi, Diego Carraro, and Andrea Visentin. 2023. "On Forecasting Cryptocurrency Prices: A Comparison of Machine Learning, Deep Learning, and Ensembles" Forecasting 5, no. 1: 196209. https://doi.org/10.3390/forecast5010010