Time Series Classification of Cryptocurrency Price Trend Based on a Recurrent LSTM Neural Network

Abstract

In this study, we applied the long short-term memory (LSTM) model to classify the cryptocurrency price time series. We collected historic cryptocurrency price time series data and preprocessed them in order to make them clean for use as train and target data. After such preprocessing, the price time series data were systematically encoded into the three-dimensional price tensor representing the past price changes of cryptocurrencies. We also presented our LSTM model structure as well as how to use such price tensor as input data of the LSTM model. In particular, a grid search-based k-fold cross-validation technique was applied to find the most suitable LSTM model parameters. Lastly, through the comparison of the f1-score values, our study showed that the LSTM model outperforms the gradient boosting model, a general machine learning model known to have relatively good prediction performance, for the time series classification of the cryptocurrency price trend. With the LSTM model, we got a performance improvement of about 7% compared to using the GB model.

1. Introduction

In the stock market, it is common to generate profit by using algorithm trading instead of direct human investment. Grove et al. [1] investigated 136 cases and concluded that mathematical models yield better results than humans. Actually, various attempts and studies have been scientifically conducted with regard to stock price prediction [2].

Numerous cryptocurrencies have been developed recently based on blockchain [3,4], and a cryptocurrency market has been formed. Especially, bitcoin is attractive in a variety of fields such as economics, cryptography, and computer science due to the unique nature of the combination of encryption technology and currency units [5,6]. A cryptocurrency market has a relatively short history compared to the stock market. Fundamentally, both stock and cryptocurrency price data have arbitrary characteristics as time series data, but the latter has higher volatility, and their prices fluctuate heavily.

A cryptocurrency market is different from the existing stock market, and it has relatively many new features [7]. Thus, in addition to the existing stock market prediction techniques, it is necessary to apply new prediction techniques suitable for the cryptocurrency market. Although many related studies have been conducted in the field of stock price, there are few studies on cryptocurrency price prediction.

The purpose of this paper is to use a deep learning model [8] to predict the price trend of cryptocurrencies without manual work. In detail, we aimed to construct our long short-term memory (LSTM) model to classify the price time series direction (price-up or price-down) for an individual cryptocurrency after a predefined time based on the past price time series changes of cryptocurrencies. In particular, we tried to explore how to construct the training and target data from cryptocurrency price time series data, so that they are suitable for input for the proposed LSTM model. We also demonstrated the LSTM model’s superiority in prediction performance by comparing the f1-score values with those of the gradient boosting model, a general machine learning model known to have relatively good prediction performance.

The rest of this paper is organized as follows: Section 2 briefly reviews some existing literature related to cryptocurrency price prediction; Section 3 discusses how to collect and preprocess the cryptocurrency price time series data and how to construct the train and target data for the LSTM model; Section 4 describes the proposed LSTM model and presents techniques for finding optimal model parameters; Section 5 outlines the evaluation results of the LSTM model’s prediction performance; Finally, Section 6 presents the conclusion.

2. Literature Review

A cryptocurrency market has many new features not found in the existing traditional stock market. Traditional stock exchanges have their own trading sessions (e.g., from 09:00 am to 15:30 pm) with no trading during state holidays or even weekends in most cases. In contrast, cryptocurrency exchanges are available 24/7, and they instantly react to any event. Thus, if one is fast enough, one can make profits via prompt transactions. Note, however, that it also means that traders should be online almost all the time lest they miss out on opportunities. On the other hand, cryptocurrencies are highly volatile compared to the traditional stock market. The cryptocurrency market is also easily manipulated unlike the stock market, so the cryptocurrency price could easily increase or decrease. Lastly, cryptocurrency trading requires the investors to store the coins themselves, and these assets are really vulnerable because new traders are unsure as to how to secure their storage. These features make the prediction of the cryptocurrency price difficult, and there is growing demand for new analytical techniques suitable for the cryptocurrency market.

Jang and Lee [7] proposed a Bayesian neural network model to predict the bitcoin price based on the blockchain information involved in bitcoin's supply and demand and verified that the latest bitcoin price has good predictive performance. Nonetheless, their model is limited to Bitcoin since the blockchain information is not easy to obtain for other cryptocurrencies.

Kim et al. [9] analyzed user comments in online social media to predict the price and number of transactions of cryptocurrencies and showed that the proposed one-dependence estimator (AODE) method is applicable to cryptocurrency trading by simulated investment. Note, however, that the method depends only on social media and does not use any past price data, which are the most credible ones for predicting the future price of cryptocurrencies.

To address the portfolio management problem, Jiang et al. [10] proposed a deep reinforcement learning method that directly produces the portfolio vector with historic cryptocurrency price data gathered from Poloniex API as input. A back-test experiment was carried out on a cryptocurrency market, and the performance was compared with 3 benchmarks and 3 other portfolio management algorithms, garnering positive results. Nevertheless, their study is hardly an individual cryptocurrency trend prediction since they proposed a portfolio management approach that determines which cryptocurrency requires heavy investment.

Radityo et al. [11] studied several multi-layer perceptron-based neural network models to predict the price of Bitcoin. Their study opens new possibilities for future deep learning research on the cryptocurrency price trend. Heo et al. [12] collected and processed several cryptocurrency price data through Bithumb API. They then used the gradient boosting (GB) model, which is a representative datadriven learning-based machine learning model, and let the model learn the price data change of cryptocurrency. They also found the most optimal model parameters in the verification step and finally evaluated the prediction performance of the cryptocurrency price trends. Their study showed that the GB model’s f1-score is at most around 0.63, which is not a high prediction performance. Note, however, that they did not use a deep learning model for the prediction and presented no comparison results between the GB model and a deep learning model.

3. Data Processing

This section describes the process of collecting cryptocurrency price data and reconstructing them for use as training data. The data is collected by Bithumb API (https://www.bithumb.com/u1/US127). They are initially mixed with various abnormal data, so they need to be preprocessed.

3.1 Data Collection and Preprocessing

We collected cryptocurrency price values every 10 minutes. The collected data has five features: open price, close price, high price, low price, and volume at each time epoch (i.e., every 10 minutes). We considered seven kinds of cryptocurrency to be used in this work: BTC (Bitcoin), ETH (Ethereum), XRP (Ripple), BCH (Bitcoin Cash), LTC (Litecoin), DASH (Dash), and ETC (Ethereum Classic), including one fiat currency, KRW (Korean Won). The price and volume data were collected from 0:00 on June 9, 2017 to 09:00 on May 8, 2018 through Bithumb API.

Table 1 shows an example of the collected raw BTC price data. The collected data includes (1) normal data (Indices 1, 2, 4, 8, and 10 in Table 1), (2) missing data, (3) empty data, and (4) non-matching data. Missing data means data that has not been collected at a time interval of 10 minutes (Indices 6 and 7 in Table 1). Empty data refers to data collected at a time interval of 10 minutes but is empty (Index 5 in Table 1). Non-matching data is data that does not fit perfectly every 10 minutes (Indices 3 and 9 in Table 1)—the time information of the non-matching data is underlined. If certain data is empty or missed, then the values of the previous normal data are copied to fill the value of the abnormal data. For example, in the case of missing data, the previous data are copied, and the time information is properly inserted; the case of empty data is also processed in the same manner. For non-matching data, if there are already normal data collected at 10-minute intervals, the non-matching data whose time is closest to the normal data is removed (Index 3 in Table 1). Otherwise, the time information of the data is updated with the time adjusted to correct 10-minute intervals (Index 9 in Table 1). Table 2 shows the preprocessed data. It has one less record than the raw data of Table 1, since the record whose index is 3 in Table 1 is removed.

Table 1. Example of the collected raw BTC price data

Table 2. Preprocessed BTC price data for the raw data of Table 1

3.2 Training and Testing Data

Our training and testing data are encoded to the three-dimensional price tensor using the preprocessed data. The price tensor is defined as similar to the one introduced in [10]. Price tensor X_t at epoch t consists of four two-dimensional matrices V_t^(c),V_t^(h),V_t^(l)​​​​​​​, and V_t^(v)​​​​​​​, which represent close price, high price, low price, and transaction volume, respectively, for every unit of time α. Open price is not included in a price tensor because it usually equals the close price of the previous time epoch. In our study, the unit of time α will be 10, 30, or 60 minutes.

The close price for epoch t of the ݅i-th cryptocurrency is denoted by v_i,t^(c). On the other hand, v_i,t^(h) is the high price data,  v_i,t^(l) is the low price data, and  v_i,t^(v) is the transaction volume of epoch t. .The 0-th cryptocurrency represents KRW (Korean Won), and its tensor value is always 1 regardless of epoch t, since we assume that it plays the role of standard currency.

\(v_{0, t}^{(h)}=v_{0, t}^{(l)}=v_{0, t}^{(c)}=v_{0, t}^{(v)}=1\)       (1)

The price tensor at a time epoch includes the past ݊ price and volume data for the unit of time α .We call ݊n the window size. If α = 30 and n = 50, price tensor X_t includes the price data during 30 × 50 = 1500 minutes. Let m be the number of cryptocurrencies including the base currency, and it is set to 8 (KRW, BTC, ETH, XRP, BCH, LTC, DASH, ETC) in this study. Fig. 1 shows the data structure of the price tensor at time epoch t for window size ݊n, the unit of time α,and the eight cryptocurrencies (i. e., m=8). When operator ⊘ is defined as element-wise vector division, the four matrices V_t^(c),V_t^(h)​​​​​​​,V_t^(l)​​​​​​​, and V_t^(v)​​​​​​​ for epoch t and 0≤i≤7 are as follows:

\(\begin{array}{l} V_{t}^{(c)}=\left[v_{i, t-n+1}^{(c)} \oslash v_{i, t}^{(c)}\left|v_{i, t-n+2}^{(c)} \oslash v_{i, t}^{(c)}\right| \cdots\left|v_{i, t-1}^{(c)} \oslash v_{i, t}^{(c)}\right| 1\right] \\ V_{t}^{(h)}=\left[v_{i, t-n+1}^{(h)} \oslash v_{i, t}^{(c)}\left|v_{i, t-n+2}^{(h)} \oslash v_{i, t}^{(c)}\right| \cdots\left|v_{i, t-1}^{(h)} \oslash v_{i, t}^{(c)}\right| \mathbf{1}\right] \\ V_{t}^{(l)}=\left[v_{i, t-n+1}^{(l)} \oslash v_{i, t}^{(c)}\left|v_{i, t-n+2}^{(l)} \oslash v_{i, t}^{(c)}\right| \cdots\left|v_{i, t-1}^{(l)} \oslash v_{i, t}^{(c)}\right| \mathbf{1}\right] \\ V_{t}^{(v)}=\left[v_{i, t-n+1}^{(v)} \oslash v_{i, t}^{(v)}\left|v_{i, t-n+2}^{(v)} \oslash v_{i, t}^{(v)}\right| \cdots\left|v_{i, t-1}^{(v)} \oslash v_{i, t}^{(v)}\right| \mathbf{1}\right] \end{array}\)       (2)

Eq. (2) shows that all the values are divided by the corresponding last price or last volume, so they are well-normalized.

Fig. 1. Data structure of price tensor at the time epoch (n : the window size, α: the unit of time, m;: thenumber of cryptocurrencies).

On the other hand, for price tensor X_t at epoch t, target (label) data X_i,t^(target) is expressed for cryptocurrency (1≤i≤7) as follows:

\(X_{i, t}^{(\text {target})}=\left\{\begin{array}{ll} 1 & \text {if } v_{i, t+\theta}(c) \\ 0 \end{array}\left(1+\frac{\varepsilon}{100}\right)>v_{i, t}^{(c)}\right.\)       (3)

For a price tensor, there are seven target data excluding KRW. It means that we will predict the price trend individually for each of the seven cryptocurrencies from their past price data. In Eq. (3), v_i,t+θ^(c) is the close price of unit of times elapsed from t to t + θ for cryptocurrency ݅i. If v_i,t+θ^(c) exceeds v_i,t^(c), by ε%, 1 (price-up) is given, or 0 (price-down) otherwise. In other words, ε is the rate of price increase after θ unit of times. In our study, θ and ε are fixed at 1 and 0.1, respectively. Therefore, if the unit of time is set to 30 minutes, the target value of a cryptocurrency at time epoch t is 1 if the cryptocurrency’s price goes over 0.1% after 30 (=1 × 30) minutes, or 0 otherwise.

4. Model Training and Validation

4.1 Model Structure

In our work, we use the LSTM model for the binary classification of the cryptocurrency price trend. As a recurrent neural network model, the LSTM model [13] determines whether the weight value is maintained by adding cell states in an LSTM cell. The LSTM model can accept arbitrary length of inputs, and it can be implemented flexibly and in various ways as required. The state obtained from an LSTM cell is used as input to the next LSTM cell, so the state of an LSTM cell affects the operation of the subsequent cells. The final target output at the end of the sequence represents a label classifying the price trend (up or down). The LSTM model has the ability to remove or add information to the cell state, carefully regulated by structures called gates, which are a way of optionally letting information through. The LSTM model is more persistent than the existing RNN because it is possible to control long-term memory.

As shown in Fig. 2, our LSTM model consists of one LSTM layer having n LSTM cells, two Dense layers, and one output layer. For time epoch t, price tensor X_t is used for input for the LSTM layer. The number of hidden units of an LSTM cell will be 32, 64, or 128. The proper number of units will be chosen by the model tuning process and explained in the next subsection. On the other hand, the numbers of hidden units at Dense I and II layers are fixed at 32, 8, and 2. Except for the last output layer using “softmax,” all LSTM and other Dense I and II layers use the activation function selected by the model tuning process, which will be explained in Section 4.2. Since the last output layer’s activation is “softmax,” the output vector has only two values added up to 1, and they can be interpreted as probabilities for price up and down trends. For 0 ≤ i ≤ 7, the last outputs \(\bar{X}_{i, t}^{(t a r g e t)}\) are compared with target data X_i,t^(target) for price tensor X_t, For loss s function LOSS_i, we use the cross entropy indicating the distance between \(\bar{X}_{i, t}^{(t a r g e t)}\) and X_i,t^(target).

Fig. 2. Proposed LSTM model structure (windows size is n and \(\hat{\nu}^{(c)}_{i,k}\;=\;\nu^{(c)}_{i,k}\;\oslash\;\nu^{(c)}_{i,t}, \hat{\nu}^{(h)}_{i,k}\;=\;\nu^{(h)}_{i,k}\;\oslash\;\nu^{(h)}_{i,t}, \hat{\nu}^{(l)}_{i,k}\;=\;\nu^{(l)}_{i,k}\;\oslash\;\nu^{(l)}_{i,t} ,\hat{\nu}^{(\nu)}_{i,k}\;=\;\nu^{(\nu)}_{i,k}\;\oslash\;\nu^{(\nu)}_{i,t} for t - n + 1 {\leq} k {\leq} t)\)

4.2 Model Tuning

A machine learning model has various hyper-parameters that determine the network structure (e.g., number of hidden units) as well as how the models are trained (e.g., type of optimizer). The performance of a model can vary considerably according to the selected set of hyper-parameters. In this study, we used the grid search method [14] to find the optimal hyper-parameters for our cryptocurrency price dataset by trying every possible combination of hyper-parameters based on the dataset. We also verified the validity of the model by performing k-fold cross-validation [15,16] in addition to finding the optimal hyper-parameters.

To demonstrate the superiority of the proposed LSTM model, we also used the GB classifier model, which is known as a traditional machine learning model showing good performance in various fields [12,17]. The GB model is an ensemble learning model for prediction by combining outputs from individual trees. It builds trees one at a time, with each new tree helping correct the errors made by the previously trained tree. It exploits the boosting scheme, which focuses step by step on difficult data samples by strengthening the impact of the successful classification. For the purpose of fairness, we also performed the same model tuning process for the GB classifier model.

Fig. 3 shows the overall process of finding the optimal set of hyper-parameters and validating the GB and LSTM models with optimal ones. First, we separate the cryptocurrency price dataset into learning and test data. Next, ݇k-fold cross-validation based on grid search is performed. In ݇k-fold cross-validation, the training dataset is randomly partitioned into ݇ k equal-sized sub-datasets. Among the ݇k sub-datasets, a single sub-dataset is retained as validation data for testing the model, and the remaining k - 1 subdatasets are used as training data. The cross-validation process is then repeated ݇ k times, with each of the ݇k sub-datasets used exactly once as validation data. The ݇k results can then be averaged to produce a single set of optimal hyper-parameters. The selected model is again trained by using the optimal hyperparameters. Finally, the model performance is measured using the test data. The performance evaluation results are presented in Section 5.

Fig. 3. Overall model tuning process with grid search-based k-fold cross-validation.

For the hyper-parameters of the LSTM model, we consider the following: (1) number of hidden units of an LSTM cell; (2) parameter initializer; (3) activation type; (4) dropout rate; and (5) optimization type. The number of hidden units of an LSTM cell is the dimensionality of the last output space of the LSTM layer. The parameter initializer represents the strategy for initializing the LSTM and Dense layers’ weight values. The activation type represents the type of activation function that produces non-linear and limited output signals inside the LSTM and Dense I and II layers. Furthermore, the dropout rate indicates the fraction of the hidden units to be dropped for the transformation of the recurrent state in the LSTM layer. Finally, the optimization type designates the optimization algorithm to tune the internal model parameters so as to minimize the cross-entropy loss function. In the LSTM model, the candidate values used to perform the grid search for the hyper-parameters are listed in Table 3. The table also lists an example of the optimal hyper-parameter values found by our model tuning process.

Table 3. Candidate and optimal sets of hyper-parameters for the LSTM model​​​​​​​

On the other hand, Table 4 shows the candidate values used to perform grid search for the GB hyperparameters and also lists the optimal hyper-parameter values. For the GB model, we consider the following: (1) maximum depth; (2) maximum features; (3) number of estimators; (4) subsamples; and (5) minimum samples for split. For the details of these hyper-parameters, refer to [17].

Table 4. Candidate and optimal sets of hyper-parameters for the GB model

5. Prediction Performance Evaluation

In this section, we evaluate the performance of the LSTM model’s binary classification and compare the LSTM model’s prediction performance against that of the GB model as evaluated in [12].

5.1 Evaluation Environment

Our evaluation task was executed on Ubuntu 16.04 LTS with 32 GB RAM and two GPU cards (NVIDIA GTX 1080Ti 11 GB). We used Tensorflow-GPU 1.8 and Keras 2.2.0 operated with Python 3.6. According to the process shown in Fig. 4, the 3-fold cross-validated grid search is first performed for the cryptocurrency price tensor data set (that is, k=3), and the optimal hyper-parameters are found through each model tuning. The model training is performed using the derived optimal hyper-parameters listed in Tables 3 and 4. For such model training, the number of learning epochs is set to 200.

Fig. 4. Performance comparison of the proposed LSTM model and the GB model [12] in terms of seven cryptocurrencies and window size = 25, 50, and 75 (unit of time α is fixed to 10).

5.2 Performance Metrics

An unambiguous and thorough way of presenting the prediction results of a deep learning model is to use a confusion matrix. Table 5 is an example of the binary confusion matrix by the LSTM model evaluation when the window size is 10. In the binary confusion matrix, true positive (TP) indicates cases wherein both actual label (i.e., price-up) and model prediction are correctly positive. False negative (FN) indicates cases wherein the actual label is positive but the model prediction is incorrectly negative (i.e., price-down). False positive (FP) indicates cases wherein the actual label is negative (i.e., not RDP) but the model prediction is incorrectly positive. Finally, true negative (TN) indicates cases wherein both actual label and model prediction are correctly negative.

Table 5. Example of binary confusion matrix for the LSTM model evaluation (݊n = 25 and α = 10)

As shown in Table 5, there is an imbalance in the number of actual target data—the number of actual positives is 7115 (=3251+3864), whereas the number of actual negatives is 3392 (=1601+1791). The accuracy measurement can be misleading when there is such an imbalance. A model can predict the target of the majority for all predictions and achieve high classification accuracy, and the model loses its usefulness. To overcome the problem of accuracy measurement, we compute additional measurements to evaluate the LSTM and GB models: recall, precision, and f1-score [18]. They are defined by using the confusion matrix as follows:

\(Recall =\frac{T P}{T P+F P}\)       (4)

\(Precision =\frac{T P}{T P+F N}\)       (5)

\(F 1-\text {score}=\frac{2 \times \text { Precision } \times \text { Recall}}{\text {Precision}+\text {Recall}}\)       (6)

The f1-score represents the harmonic mean of precision and recall and indicates the classification performance of a model relatively accurately. It is expressed in the range of 0–1, where the best value is 1. We compute the recalls, precisions, and f1-scores, and then finally get a single f1-score measurement for the performance evaluation of the LSTM and GB models.

5.3 Evaluation Results

The evaluation is performed to compare the performance of the LSTM and GB models and show the superiority of the LSTM model for predicting the cryptocurrency price trend. The GB model is used in [12], and we also evaluate the GB model’s performance according to [12]. Fig. 5 shows the comparison of the f1-score values for the two models with the seven cryptocurrencies in terms of the window size of the price tensor. It can be seen that the LSTM model is always better than the GB model for all cryptocurrencies and the window sizes tested. The f1-score values of the LSTM model are between 0.63 and 0.68, whereas those of the GB model are between 0.59 and 0.63. It indicates that a performance improvement of about 7% can be expected with the LSTM model.

Fig. 5. Performance comparison of the proposed LSTM model and the GB model [12] in terms of sevencryptocurrencies and window size = 25, 50, and 75 (unit of time α is fixed to 10).

As shown in Fig. 5, it is difficult to find the performance distribution tendency according to the window size. The LSTM model best predicts the price trend when the window size is just 25 for BCH, DASH, and ETC and 50 for XRP and LTC. For BTC and ETH, the prediction performance is highest when the window size is 75. Still, we can know that a large amount of data with long window size does not guarantee high performance. We can also deduce that DASH is the best cryptocurrency for the LSTM model to predict the price trend.

Fig. 6 illustrates the comparison of the f1-score values for the LSTM and GB models with the seven cryptocurrencies in terms of unit of times. Similar to the results shown in Fig. 5, we can also know that the LSTM model is always better than the GB model for all cryptocurrencies and units of time tested. With the LSTM model, we can expect a performance improvement of about 7% compared to using the GB model.

Fig. 6. Performance comparison of the proposed LSTM model and the GB model [12] in terms of sevencryptocurrencies and unit of times = 10, 30, and 60 (window size n is fixed to 25).

As shown in Fig. 6, it is also difficult to find the performance distribution tendency according to the unit of time. The LSTM model best predicts the price trend when the unit of time is just 10 for BTC, ETH, and BCH and 30 for XRP, DASH, and ETC. For LTC, the prediction performance is highest when the unit of time is 60. Finally, we can also know that DASH is the best cryptocurrency for the LSTM model to predict the price trend, followed by XRP.

6. Conclusion

In this study, we applied the LSTM model to classify the cryptocurrency price time series. We collected historic cryptocurrency price time series data via Bithumb API, preprocessed them, and encoded the clean data into the three-dimensional price tensor. We also presented our LSTM model structure as well as how to use such price tensor as input data of the LSTM model. In particular, our model tuning scheme was provided to find the most suitable LSTM model parameters. The results of the prediction performance show that XRP and DASH are relatively predictable, whereas BCH is relatively hard to predict. Moreover, it can be seen that there is no significant difference in the prediction performance according to the window size and unit of time. We have also demonstrated that the LSTM model has a better f1-score than the GB model. Despite using a simple LSTM model, the average f1-score is approximately 0.68 for DASH, whereas the corresponding f1-score of the GB model is only about 0.63. Therefore, the LSTM model is relatively suitable when classifying the cryptocurrency time series data with high volatility. In future work, we plan to use additional features (e.g., mining hash rate) to build a better LSTM model so that the model raises the f1-score further.