International Review of Financial Analysis 92 (2024) 103055

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International Review of Financial Analysis

journal homepage: www.elsevier.com/locate/irfa

Cryptocurrency price forecasting – A comparative analysis of ensemble

learning and deep learning methods
Ahmed Bouteska, Mohammad Zoynul Abedin *, Petr Hajek, Kunpeng Yuan
a
Finance, Faculty of Economics and Management of Tunis, University of Tunis El Manar, Tunisia
b
School of Management, Swansea University, Bay Campus, Fabian Way, Swansea SA1 8EN, Wales, United Kingdom
c
Science and Research Centre, Faculty of Economics and Administration, University of Pardubice, Studentska 84, 532 10 Pardubice, Czech Republic
d
School of Economics and Management, Dalian University of Technology, No.2, Linggong Road, Liaoning, 116024 Dalian, China

A R T I C L E I N F O A B S T R A C T

Keywords: Cryptocurrency price forecasting is attracting considerable interest due to its crucial decision support role in
Cryptocurrency investment strategies. Large fluctuations in non-stationary cryptocurrency prices motivate the urgent need for
Bitcoin accurate forecasting models. The lack of seasonal effects and the need to meet a number of unrealistic re­
Forecasting
quirements make it difficult to make accurate forecasts using traditional statistical methods, leaving machine
Ensemble learning
Deep learning
learning, particularly ensemble and deep learning, as the best technology in the area of cryptocurrency price
Neural networks forecasting. This is the first work to provide a comprehensive comparative analysis of ensemble learning and
deep learning forecasting models, examining their relative performance on various cryptocurrencies (Bitcoin,
Ethereum, Ripple, and Litecoin) and exploring their potential trading applications. The results of this study
reveal that gated recurrent unit, simple recurrent neural network, and LightGBM methods outperform other
machine learning methods, as well as the naive buy-and-hold and random walk strategies. This can effectively
guide investors in the cryptocurrency markets.

1. Introduction Therefore, cryptocurrencies provide investors with diversification and

hedging opportunities. As of 2022, there are >20,000 cryptocurrencies,
The area of cryptocurrencies has attracted growing attention from but only the top 20 account for nearly 90% of the total market. The
investors and regulators since Bitcoin was introduced in 2008 (Corbet global cryptocurrency market capitalization was 1.06 trillion USD, with
et al., 2019). This growing popularity of cryptocurrencies is related to >300 million cryptocurrency users around the world in 2022 (Tuwiner,
their different characteristics from other traditional financial assets. 2022).
Their value is based on the confidence of the underlying algorithm, Large price fluctuations of cryptocurrencies generate huge profit
rather than on any tangible asset, allowing cryptocurrencies to be in­ opportunities for high-frequency traders, including algorithmic trading
dependent of any higher authority. This is what eventually leads to low bots (Chu et al., 2019; Chu et al., 2020; Patel et al., 2015). It is estimated
transaction costs and government-independent secure peer-to-peer that more than half of the trading volume is accounted for by these bots,
payments. making it increasingly difficult for human traders to make profit when
Extant research recognizes cryptocurrencies as an investment asset trading during short periods (Ibrahim et al., 2021). These bots are aided
(Bouri et al., 2017; Corbet et al., 2019; Ji et al., 2018). In response, a by increasingly complex machine learning methods, frequently backed
nascent strand of literature has appeared to explore the potential syn­ by deep learning (Rahmani Cherati et al., 2021).
ergies between cryptocurrencies and other investment assets, such as The purpose of developing cryptocurrency price forecasting systems
commodities (Das et al., 2020), equities (Jiang et al., 2021), and con­ is to develop a model that can guide the algorithmic/human trader in
ventional currencies (Shahzad et al., 2022). Notably, Guesmi et al. trading decisions to increase the chances of making profits when trading
(2019) underlined how Bitcoin allows hedging investment strategy cryptocurrencies. Different cryptocurrency price forecasting methods
against various investment assets, including gold, oil, and equities, due can be divided into traditional statistical methods and machine learning
to its high return and low correlation with the other investment assets. methods (Chen et al., 2021).

* Corresponding author.
E-mail address: m.z.abedin@swansea.ac.uk (M.Z. Abedin).

https://doi.org/10.1016/j.irfa.2023.103055
Received 17 December 2022; Received in revised form 28 November 2023; Accepted 18 December 2023
Available online 27 December 2023
1057-5219/© 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

Early work in this area focused primarily on traditional statistical performance of the hybrid two-step forecasting method (Efat et al.,
methods, such as ARIMA (autoregressive integrated moving average) 2022) that combines ARIMA with deep learning methods, thus capturing
(Ibrahim et al., 2021) and GARCH (Baur et al., 2018; Fakhfekh and linear and nonlinear patterns in the cryptocurrency time-series data.
Jeribi, 2020). However, these approaches only capture linear patterns in More importantly, the comparative analysis includes the financial per­
the time series of cryptocurrencies and furthermore assume a normal formance of trading strategies based on the machine learning methods
distribution of variables, which is unrealistic in the case of crypto­ utilized. Thus, this work provides valuable insights into the performance
currencies (Chen et al., 2021; Khedr et al., 2021). of different machine learning models for predicting cryptocurrency
Machine learning approaches can extract nonlinear patterns and also prices, and their potential applications in trading strategies. The results
benefit from large datasets without assuming any prior understanding of suggest that these models can enable investors to make more informed
the data. However, even traditional machine learning methods, such as decisions in the cryptocurrency markets, ultimately leading to better
multilayer perceptron (MLP) neural networks (Kristjanpoller and Min­ investment outcomes.
utolo, 2018) or support vector machines (SVM) (Hajek et al., 2023; The remainder of the article is organized as follows. Section 2 pro­
Moula et al., 2017), suffer from some problems such as susceptibility to vides an overview of previous literature on cryptocurrency price fore­
overfitting and do not fully exploit the potential of extracting high-level casting. Section 3 presents the research methodology employed and
hidden patterns from cryptocurrency sequential data. To overcome Section 4 shows the results. This is followed by Section 5, which dis­
these problems, deep learning-based forecasting models have been used, cusses the results. Section 6 concludes the study with some future
having the capacity to outperform traditional machine learning methods research directions.
(Chen et al., 2021; Cui et al., 2022; Liu et al., 2021; Ortu et al., 2022).
The recent work of Murray et al. (2023) substantiates this finding, 2. Literature review
demonstrating that long short-term memory (LSTM) and gated recurrent
unit (GRU) neural networks outperform various other statistical and In theory, the value of cryptocurrencies is a reflection of their utility
machine learning methods in terms of forecasting error. This includes as a medium of exchange, which considerably increased over the last ten
not only traditional models such as ARIMA and SVM but also the more years. Given the increasing importance of cryptocurrencies for financial
contemporary temporal fusion transformer (TFT). Another stream of systems, early work in this area focused primarily on cryptocurrency
research has focused on the capacity of ensemble learning approaches to volatilities, which have proved to be large (Klein et al., 2018) and
reduce variance and bias by combining a set of diverse weak learning difficult to predict so far (Fang et al., 2020; Walther et al., 2019).
models (Aggarwal et al., 2020). In their widely acclaimed work, Sun Moreover, empirical evidence also suggests that (Zhang et al., 2018): (1)
et al. (2020) showed that ensemble learning forecasting models cryptocurrency returns have heavily tailed distributions, (2) autocor­
outperform individual machine learning models and that gradient relations for relative and absolute returns decay at different rates; (3)
boosting demonstrates better accuracy and robustness compared with cryptocurrencies exhibit a strong leverage effect and volatility clus­
the well-known random forest approach. tering; (4) volatility and returns show the long-range dependence; and
Not only does the existing literature fail to provide a comprehensive (5) volatility and price are power-law correlated. These characteristics
comparison of the latest machine learning methods, but previous studies make cryptocurrency price forecasting challenging and investments in
also suggest that different methods may perform differently for different cryptocurrencies much riskier than investments in traditional financial
cryptocurrencies (Yang et al., 2020; Zhang et al., 2021). Moreover, no assets. Fluctuations in the value of cryptocurrency assets have been
comparative study has been found that examines the financial perfor­ difficult to predict because they are not related to any fundamentals,
mance of cryptocurrency investors from the perspective of different which leads to the hypothesis that the value is mainly influenced by the
trading strategies over different time periods. To bridge this gap, this sentiment of the cryptocurrency market. As shown in the literature, the
work aims to assess the performance of state-of-the-art deep learning price of Bitcoins and many other cryptocurrencies has displayed cycli­
and ensemble learning approaches in forecasting the prices of four major cality patterns (also referred to as bubbles) in recent years (Dong et al.,
cryptocurrencies, namely Bitcoin, Ethereum, Ripple, and Litecoin. The 2022; Kyriazis et al., 2020).
selection of these four cryptocurrencies is not only consistent with those Most of the research on cryptocurrency price forecasting has focused
in previous related studies (Altan et al., 2019; Cheng, 2023) but it also on conventional statistical methods. Catania et al. (2019) used a battery
covers a wide range of technologies, applications and market positions, of univariate and multivariate vector autoregression (VAR) models for
making them ideal subjects for comprehensive analysis and forecasting. predicting four major cryptocurrencies: Bitcoin, Ripple, Litecoin, and
In particular, predicting the price of Ethereum can provide insights into Ethereum. Notably, significant improvements in forecasting accuracy
a wider range of blockchain applications, predicting the price of Ripple were reported for the combinations of various univariate forecasting
can provide valuable insights into the integration of cryptocurrency models. Conrad et al. (2018) analyzed the volatility of cryptocurrencies
technologies into traditional banking systems, and predicting the price through the lens of GARCH-MIDAS model to extract the long and short-
of Litecoin alongside Bitcoin can reveal how changes in blockchain term volatility components, finding that S&P 500 volatility significantly
technology affect cryptocurrency market performance. This diversity affected long-term Bitcoin volatility. Likewise, Walther et al. (2019)
ensures that the study's findings will be broadly relevant and provide applied the GARCH-MIDAS framework to forecast the volatilities of five
valuable insights into the dynamics of the cryptocurrency sector. highly capitalized cryptocurrencies as well as the CRIX cryptocurrency
Furthermore, in contrast to earlier research that has tended to evaluate index, investigating the effect of Global Real Economic Activity as a
the forecasting performance in terms of forecasting errors (Chen et al., major driver of long-term cryptocurrency volatility. Results reported by
2021; Murray et al., 2023), here we focus on investor performance by Walther et al. (2019) also suggest that the traditional GARCH model
simulating the buy & sell, long and short trading strategies. To this end, performs poorly in predicting cryptocurrency volatility during bear
two distinct sub-periods are considered in this study, before and after markets, being surpassed even by models based on individual exogenous
Covid-19. Indeed, the Covid-19 pandemic has had a significant impact variables.
on the cryptocurrency market, including changes in market efficiency, Over the last five years, the focus of cryptocurrency price forecasting
peak performance of some cryptocurrencies, and increases in market has shifted to machine learning methods. The work of Kristjanpoller and
capitalization (El Montasser et al., 2022; Jalan et al., 2021). To this line Minutolo (2018) has made a significant contribution to the field by
of research, this study adds an analysis of the predictability of crypto­ proposing a hybrid MLP neural network-GARCH model to forecast the
currencies in the pre- and post-pandemic period. Unlike previous price volatility of Bitcoin. The results of a thorough analysis of different
comparative studies that have focused only on the combinations of deep GARCH models revealed the benefits of combining linear and nonlinear
learning models (Murray et al., 2023), this paper also examines the models for predicting Bitcoin price volatility. MLP neural network was

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A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

also employed by Nakano et al. (2018) for predicting Bitcoin returns the relevance of ensemble learning and deep learning for automatic
based on a set of technical indicators. Experimental evidence showed cryptocurrency trading.
that the MLP forecasting model outperforms the baseline buy-and-hold
strategy. MLP also performed well when comparing its movement di­ 3. Research methodology
rection performance against ARIMA, Prophet, and random forest
(Ibrahim et al., 2021). More recently, recurrent neural networks have In this section, the methods used for the construction of forecasting
been utilized, such LSTM and GRU, to automatically extract high-level models are introduced, together with their specifications. The machine
temporal patterns from cryptocurrency time series. These advanced learning methods employed in this study include boosting-based
neural networks with deep learning were specifically developed to ensemble methods, recurrent deep neural networks, and hybrid two-
handle complex sequential data and, therefore, it was not surprising that stage methods integrating ARIMA with recurrent deep neural networks.
MLP and other conventional machine learning methods were out­
performed by LSTM in several studies (Chen et al., 2021; Lahmiri and 3.1. Boosting-based ensemble methods
Bekiros, 2019; Li and Dai, 2020).
GRU also produced excellent forecasting performance for four major Given that bagging-based ensemble methods, including random
cryptocurrency prices (Zhang et al., 2021), outperforming not only forest, have not performed well in earlier research (Ibrahim et al., 2021;
traditional machine learning methods but also LSTM-based models. Sun et al., 2020), we decided to examine the performance of boosting-
However, these deep learning-based models have been shown to work based ensemble methods in the current study. The ultimate aim of
effectively, especially in univariate settings (Uras et al., 2020) because boosting is to enhance the accuracy of a sequence of weak prediction
they are not equipped with a feature selection component and therefore models, where each model in the sequence compensates for the errors of
can easily become too complex to learn more challenging temporal its predecessors. As a result, a strong model is produced representing a
patterns (Fu et al., 2022). highly accurate combination of weak models. This approach not only
Ensemble learning methods represent a viable alternative to deep proved to be effective compared with individual and other ensemble
learning models due to their capacity to reduce the bias (boosting learning methods, but also outperformed deep learning models in recent
methods) or variance (bagging methods such as random forest) of in­ investigations (Manchanda and Aggarwal, 2021). Noteworthy, Ada­
dividual machine learning methods (Derbentsev et al., 2020). The model Boost, a traditional boosting approach, exceeded the forecasting per­
based on LightGBM (light gradient boosting machine) demonstrated the formance of LSTM and other machine learning methods, including MLP
capacity to outperform the random forest model in forecasting the price and ELM (extreme learning machines) (Manchanda and Aggarwal,
direction of the cryptocurrency market (Sun et al., 2020), thus sug­ 2021).
gesting that bias reduction is more relevant in the case of cryptocurrency The idea of AdaBoost is that the weights of the data instances that are
prices than variance reduction. Overall, the above studies indicate that accurately predicted by the preceding weak regressor are decreased
the machine learning-based forecasting models outperform those using while the weights of the instances where forecasts deviated from the
conventional statistical methods. This is attributed to the capacity of actual cryptocurrency prices are increased. Thus, successive forecasting
machine learning models to construct generic models easily capturing models increasingly focus on poorly forecasted data instances, and the
nonlinear complex patterns in cryptocurrency data. Recently, there have performance of the overall model is iteratively improved. In other
been two attempts to systematically review the performance of machine words, AdaBoost generates an additive model while the value of loss
learning methods for cryptocurrency price forecasting (Khedr et al., function (bias) is reduced in each iteration.
2021; Ren et al., 2022). Khedr et al. (2021) concluded that LSTM is LightGBM is an enhanced version of AdaBoost, allowing for the
considered to be the best method for predicting cryptocurrency price computationally efficient minimization of an arbitrary differentiable
time series due to its ability to recognize long-term time-series associ­ loss function. Similarly, as AdaBoost, regression trees are employed as
ations. Ren et al. (2022) also valued the predictive performance of LSTM weak learners in LightGBM. In contrast, the fast and highly efficient
while highlighting that combining different machine learning methods training capacity of LightGBM allows for dealing with large datasets.
has now become a hot research area. While these survey studies focus on This is enabled by exploiting the exclusive feature bundling (into a
providing an overview of existing machine learning methods used for single feature and thus reducing data dimensionality) and gradient-
cryptocurrency price forecasting, this study seeks to conduct a based one-side sampling (by randomly dropping instances with small
comparative empirical analysis of state-of-the-art deep learning and gradients). At the same time, the advantages of the well-known XGBoost
ensemble learning methods to provide support for profitable algorithmic (extreme gradient boosting) are retained, including parallel training,
trading. sparse optimization, multiple loss functions, early stopping, and regu­
Algorithmic trading has been actively developing in recent decades larization. The main difference is that LightGBM grows regression trees
due to a combination of factors: the rapid development of machine leafwise, and not level-wise like traditional boosting methods. The
learning methods, the development of technologies for working with objective function of LightGBM is defined as follows:
data and its analysis, the growth of storage and processing capabilities ((∑ )2 (∑ )2 (∑ )2 )
for large amounts of data. In addition, the complexity of trading system gi gi gi
G = 1 2 ∑ i∈IL
/
+ ∑ i∈IR − ∑ i∈I (1)
algorithms used by market participants is growing, since they compete i∈IL hi + λ i∈IR hi + λ i∈I hi + λ
not only with those who do not use automated systems, but also with
each other. In connection with these trends, the study of the applica­ where IR and IL are the sets of instances of the right and left branches,
bility of various machine learning algorithms to algorithmic trading respectively; gi and hi represent the loss gradient statistics of the first and
problems is an urgent task. This is important not only for companies second order, respectively; and λ is a regularization parameter.
engaged in algorithmic trading, such as hedge funds, but also from the
scientific community because the application of state-of-the-art machine 3.2. Recurrent deep neural networks
learning algorithms to the area under consideration can bring new
knowledge to the development of automated trading systems for cryp­ Recurrent neural networks (RNNs) are types of neural networks in
tocurrency markets. This paper is devoted to the application of ensemble which links between units generate a controlled sequence, which allows
learning and deep learning to forecast cryptocurrency prices. In cryp­ for processing sequential data. In contrast to MLP, RNN can process
tocurrency market trading, both the base predictors in ensembles and arbitrary length sequences with its internal memory. Various RNN ar­
neural networks with deep learning mimic the actions of trading agents chitectures, ranging from simple to complex, have been introduced. For
on the cryptocurrency market. This study was carried out to investigate cryptocurrency price forecasting, the LSTM and GRU neural networks

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A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

are the most widely used. RNNs, equipped with a self-feedback mech­ Table 1
anism, have the capacity to handle long-term dependencies in crypto­ Values and ranges of model hyper-parameters.
currency time-series data. The vanishing gradient represents a major Models Hyper-parameters
limitation of RNNs. To overcome this problem, LSTM neural networks
MLP Hidden layers: [1,2]; the number of hidden units: [10, 20, 30, 40, 50,
were introduced (Yu et al., 2019). Each unit of LSTM is composed of 100]; activation function: [‘relu’, ‘tanh’]; optimizer solver: [‘sgd’,
memory cells that store information updated through the input, forget, ‘adam’]; regularization alpha: [0.0001], learning rate for sgd optimizer:
and output gate. At day t, xt represents the input cryptocurrency price [‘constant’，’invscaling’, ‘adaptive’].
data of the LSTM cell whose output at the previous day is denoted as LSTM Hidden layers: [1, 2]; the number of epochs: [3, 5, 10, 50, 100, 300]; the
number of hidden units [4, 8, 16, 32, 64, 128, 256]; learning rate
ℎt− 1, ct stands for the memory cell value. The calculation process of the [0.001, 0.01, 0.1]; lag days [3, 5, 8, 10]
LSTM unit is conducted as follows: AdaBoost The number of estimators: [10, 20, 30, 40, …, 100]; learning rate:
[0.001, 0.01, 0.1, 1.0]; loss functions: [linear, square, exponential]
it = (Wxi xt + Wℎi ℎt− 1 + Wci ct− 1 + bi ) (2) LightGBM The number of estimators: [10, 20, 30, 40, …, 100]; learning rate:
( ) [0.001, 0.01, 0.1, 1.0].
ft = Wxfxt + Wℎf ℎt− 1 + Wc fct− 1 + bf (3) RNN The number of units: [4, 16, 32, 64, 128].
GRU Hidden layers: [1, 2]; the number of epochs: [3, 5, 10, 50, 100, 300]; the
number of hidden units [4, 8, 16, 32, 64, 128, 256]; learning rate
ct = ft ct− 1 + it tanℎ (Wxc xt + Wℎc ℎt− 1 + bc ) (4)
[0.001, 0.01, 0.1].

ot = (Wxo xt + Wℎoℎt − 1 + Wco ct− 1 + bo ) (5)

problems, machine learning methods tend to be complex and may lack
ℎt = ot tanℎ (ct ) (6) the transparency needed to receive widespread acceptance. Classical
MLP neural network models are also not good enough to capture both
where it, ft and ot is the output of the input forget, and output gate,
linear and nonlinear patterns equally well. Therefore, here we combine
respectively and their corresponding weight matrices are Wi, Wf and Wo;
ARIMA for estimating the linear component Lt and the above-mentioned
ct is the state of the memory cell; b is bias; and σ and tanh represent
LSTM recurrent deep neural network for estimating the residual et from
sigmoid and hyperbolic tangent activation functions, respectively.
the linear model, that is, the nonlinear component Nt.
Benefitting from memory cells and control gates, LSTM builds a long-
term delay between input and feedback. The internal state of memory
cells retains a continuous flow of error, without the gradient exploding 3.4. Specifications of models
or disappearing. Similarly, GRU consists of the update and reset gates
and a memory cell, whose outputs ut, rt and ct, respectively, can be ob­ For both the boosting-based ensemble methods (AdaBoost and
tained as follows: LightGBM regressor methods) and recurrent deep neural networks
ut = (Wux xt + Wuc ct− 1 + bu ) (7) (simple RNN, GRU, and LSTM), grid search with a rolling window cross-
validation (Bhattacharjee et al., 2022; Fuss and Koller, 2016) under
rt = (Wrc xt + Wrc ct− 1 + br ) (8) minimizing the mean square error was used to find the optimal values of
the hyper-parameters, as is shown in Table 1.1
c t = tanh(Wcx ht + Wrc (rt ct− 1 ) + bc )
̂ (9) For both boosting methods, two hyper-parameters were examined,
the number of estimators and learning rate, for the LightGBM method,
ct
ct = (1 − ut )ct− 1 + ut ̂ (10) three types of loss functions were considered. For the simple RNN,
different numbers of units were tested from. For the GRU and LSTM
where ̂c t is a candidate state of the memory cell. In GRU, the reset gate is models, the following values of hyper-parameters were examined: hid­
used to select the optimal time lag. Having fewer computational pa­ den layers, number of epochs, number of hidden units, and learning rate.
rameters than LSTM, GRU proved to be more effective when handling Overall, the least complex models were generated for Litecoin (with one
less frequent and smaller datasets, such as cryptocurrency price times­ hidden layer and 8 units) while most complex models were optimal for
eries (Hansun et al., 2022). Inspired by this finding, we also consider a the Ethereum data (using 128 or 256 units in the hidden layers).
simple RNN in this study to exploit its computational efficiency. The Generally, 5 epochs were enough to train the deep learning-based
simple RNN is defined as follows: forecasting models.
ℎt = tanℎ(Wℎx ℎt− 1 + Wℎℎ xt− 1 + bℎ ) (11) In the hybrid two-stage models, the parameters of ARIMA were
selected semi-automatically by using the smallest value of BIC (Bayesian
(
yt = tanℎ Wℎy ℎt + by
)
(12) information criterion) on training data. For Ripple and Litecoin, the
ARIMA models were ARIMA(1,0,1) and ARIMA(2,0,0), respectively.
where Wh represents the weight matrix in the hidden layer, and ht and yt When the best model was represented by white noise, the restricted AR
are the outputs of the hidden and output layer, respectively. model was chosen based on the value of PACF (partial autocorrelation
function). Hence, AR (6) and AR (2) were the best models for Bitcoin and
Ethereum, respectively.
3.3. Hybrid two-stage models
4. Empirical results
The idea of a hybrid two-stage cryptocurrency price forecasting
model has its roots in the seminal paper of Zhang (2003). The idea is to
The daily cryptocurrency time-series data were collected from
use a deep neural network to estimate the residuals of the ARIMA model,
https:/www.investing.com.2 To investigate the predictability of the
with ARIMA capturing the linear patterns of the cryptocurrency price
data while a deep neural network LSTM is used to model the remaining
nonlinear patterns, thus improving the accuracy of forecasts. 1
The models were implemented in Python using the Scikit-Learn (ensemble
The ARIMA model is effective in detecting linear patterns in time- methods), Statsmodels (ARIMA), and Keras (recurrent deep neural networks)
series data. The assumption of a linear data generation process is un­ libraries. The code is provided in the supplementary material.
realistic for cryptocurrency time-series data, and it is a major limitation 2
All data used are freely accessible and downloadable at https://www.in
of the ARIMA model. At the same time, despite their rapid development vesting.com/crypto/. The data used in this study are also available in the
and reasonably successful application to real-world forecasting supplementary material.

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A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

Table 2
Data description.
Cryptocurrency Starting Midpoint date (Covid-19 Ending date No. of observations before midpoint date No. of observations after midpoint date
date timepoint) (before Covid-19) (after Covid-19)

Bitcoin April 1, January 1, 2020 August 31, 1370 1339

2016 2023
Ethereum April 1, January 1, 2020 August 31, 1370 1339
2016 2023
Litecoin April 1, January 1, 2020 August 31, 1370 1339
2016 2023
Ripple April 1, January 1, 2020 August 31, 1370 1339
2016 2023

Fig. 1. Logarithmic cryptocurrency prices.

most relevant cryptocurrencies in terms of volume, four most popular partitioned into a training set and testing set following a rolling window
cryptocurrencies were selected for our comparative analysis, namely to match the structure of the time series data, the number of rolling test
BTC/USD, ETH/USD, LTC/USD, and XRP/USD. The trading data was samples is shown in Table 2. Consistent with earlier studies (Corbet
obtained up to August 31, 2023. Table 2 presents the basic character­ et al., 2022; Livieris et al., 2021), this paper applied the first-order dif­
istics of the cryptocurrency data, and Fig. 1 shows the fluctuation of the ferences of daily cryptocurrency logarithmic prices (Fig. 2). It should be
logarithmic cryptocurrency prices. Note that each time series was split noted that while differencing can be a useful approach to dealing with
into two different sub-periods (denoted as before Covid-19 and after non-stationarity in time series data, it does not necessarily eliminate the
Covid-19), given the considerable effect of Covid-19 on cryptocurrency need for complex machine learning models. Complex machine learning
markets. models are often able to capture more complex patterns, handle larger
entire available period was considered as presented in Table 2. datasets, and automatically extract relevant features from the data. In
In the experimental setting, the rolling window cross-validation addition, they can be effective in dealing with complex relationships and
approach (Bhattacharjee et al., 2022; Fuss and Koller, 2016) was used non-linear dynamics that may not be adequately captured by traditional
to split the time series into the training set immediately followed by the quantitative techniques (Shajalal et al., 2023).
testing set. Specifically, the cryptocurrency time-series data were The summary descriptive statistics for the cryptocurrency time series

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A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

Fig. 2. First-order differences of daily logarithmic cryptocurrency prices.

Table 3
Summary descriptive statistics for cryptocurrency data.
Cryptocurrency Mean Minimum Maximum St.Dev. Skewness Kurtosis

Bitcoin 0.001526 − 0.49728 0.227602 0.038855 − 0.84402 13.01061

Ethereum 0.001829 − 0.58964 0.258599 0.053355 − 0.59340 9.05271
Litecoin 0.001102 − 0.48208 0.591547 0.056149 0.404124 12.22713
Ripple 0.001559 − 0.65299 1.027995 0.068411 2.056983 33.64264

are presented in Table 3. As can be seen in Table 3, the average daily ensemble learning and deep learning methods, two sets of metrics were
price differences were positive for all the four cryptocurrencies, with used. First, commonly used regression metrics were employed as fol­
Ethereum showing the highest returns, while Ripple showed the highest lows: MAPE (mean absolute percentage error), ME (mean error), MAE
standard deviation. In addition, the high kurtosis of all cryptocurrency (mean absolute error), MPE (mean percentage error), RMSE (root mean
data indicates leptokurtic time series, with Ethereum showing the square error), R (correlation coefficient), and MIN-MAX error. Second, a
highest excess kurtosis. Finally, while the price differences of Bitcoin set of metrics useful for evaluating investor performance was used,
and Ethereum were negatively skewed (with a longer left tail), the namely scalar product (SP), return score (Return), long return
opposite result can be observed for the price differences of Litecoin and (Return_long), short return (Return_short), mean directional accuracy
Ripple. (MDA), mean directional accuracy positive (MDA+), and mean direc­
To consider the stochastic nature of neural networks, hereinafter the tional accuracy negative (MDA-). The SP of the actual and forecast
results for the used neural networks are reported as an average of 50 values was used to simulate the buy & sell trading strategy, where the
simulation runs. As the datasets varied in terms of sample sizes amount of investment is proportional to the forecast signal. The return
(Table 2), the comparison of the forecasting performance of the used score was used to simulate the trading strategy based on the signals of
methods between different cryptocurrencies is difficult. To consider this the used ensemble learning and deep learning methods. The return score
limitation into account, three naive algorithms were employed to was calculated as the sum of the returns of a particular trading strategy.
represent benchmarks. To this end, in agreement with previous studies The long (short) return simulated the return obtained using the long
(Akyildirim et al., 2021; Caporale et al., 2018; Oyedele et al., 2023), the (short) trading strategy. MDA compares the predicted price direction
following methods were used: random walk (RW), white noise (WN), (upward or downward) to the actual cryptocurrency price direction,
and buy & sell (B&S). The random walk method is based on the while MDA+ and MDA- evaluate the upward and downward directional
Martingale assumption, hence using the last value of cryptocurrency accuracy, respectively.
price as the forecast for the next day value. The white noise method In addition to the three naive methods, several other baseline
relies on a randomly generated cryptocurrency time series with normal methods were used to demonstrate the efficiency of the deep learning
distribution; that is, with the mean calculated as the mean of the training methods, including the traditional ARIMA, MLP, and hybrid two-stage
sample and the variance being equal to the variance of the training ARIMA+MLP methods. Five and ten previous cryptocurrency prices
sample. The buy & sell method replicates a simple strategy of buying a were examined in the experiments and the best results are presented
cryptocurrency for a fixed amount of money every day and selling it at hereinafter.
the end of the day. The results of the experiments are presented in Tables 4–7. From
To comprehensively evaluate the forecasting performance of the Tables 4–7, it can be noted that the compared methods performed

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Table 4
Results of Bitcoin forecasting performance – regression and investor metrics.
Before Covid-19 (2016-04-01 to 2019-12-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX

WN 2.3206 0.0018 0.0326 1.2303 0.0427 − 0.0028 0.0536

RW 4.2513 0.0027 0.0421 0.0653 0.0518 − 0.0339 − 0.0089
B&S – – – – – – –
ARIMA 2.0730 0.0016 0.0314 1.4435 0.0398 − 0.0392 0.0425
MLP 1.7589 0.0009 0.0233 1.0032 0.0307 0.4884 0.0341
LSTM 1.0865 0.0013 0.0272 1.0103 0.0361 − 0.2352 0.1010
ARIMA+MLP 2.5503 0.0013 0.0286 1.3667 0.0364 0.2944 0.0489
ARIMA+LSTM 2.2950 0.0014 0.0301 1.4338 0.0380 0.1745 0.0556
AdaBoost 1.5506 0.0009 0.0221 0.9405 0.0294 0.5522 0.0639
LightGBM 1.5608 0.0008 0.0205 0.7688 0.0280 0.6067 0.0618
Simple RNN 1.6677 0.0012 0.0258 1.1060 0.0343 0.2629 0.0583
GRU 1.6831 0.0011 0.0250 0.9890 0.0328 0.3766 0.0427
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN − 0.0074 − 0.2021 − 0.1136 − 0.0886 52.06 52.63 51.52
RW 0.3703 − 0.4271 − 0.2260 − 0.2010 49.48 49.47 49.49
B&S − 0.0250 0.1703 2.5727 − 2.5977 53.21 100.00 0.00
ARIMA 0.6979 0.0879 0.0314 0.0565 46.39 50.53 42.42
MLP 0.2905 2.4917 1.2333 1.2584 63.40 65.26 61.62
LSTM − 0.2798 − 1.0300 − 0.5275 − 0.5025 43.81 36.84 50.51
ARIMA+MLP 0.3896 1.6641 0.8196 0.8446 58.76 62.11 55.56
ARIMA+LSTM 1.9158 0.4368 0.2059 0.2309 49.48 66.32 33.33
AdaBoost − 0.3511 2.4100 1.1925 1.2175 63.40 60.00 66.67
LightGBM − 0.3891 3.1973 1.5861 1.6111 70.62 67.37 73.74
Simple RNN 0.5778 1.2719 0.6234 0.6484 54.12 57.89 50.51
GRU 0.0796 1.8492 0.9121 0.9371 61.34 63.16 59.60

After Covid-19 (2020-01-01 to 2023-08-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX
WN 2.3029 0.0010 0.0251 1.2868 0.0323 0.0854 0.0429
RW 3.4430 0.0016 0.0324 0.8488 0.0406 0.0469 − 0.0028
B&S – – – – – – –
ARIMA 1.5634 0.0009 0.0233 1.0570 0.0301 − 0.0489 0.0486
MLP 1.7886 0.0010 0.0248 0.5186 0.0322 − 0.1178 0.0368
LSTM 1.2102 0.0009 0.0231 1.0695 0.0295 − 0.2766 0.0691
ARIMA+MLP 1.5049 0.0007 0.0202 0.4260 0.0260 0.4178 0.0200
ARIMA+LSTM 1.5597 0.0008 0.0219 0.9105 0.0281 0.2511 0.0416
AdaBoost 1.2122 0.0005 0.0170 0.3978 0.0223 0.6160 0.0476
LightGBM 1.4518 0.0005 0.0168 0.2916 0.0221 0.6234 0.0486
Simple RNN 2.1846 0.0008 0.0223 0.4604 0.0286 0.2939 0.0180
GRU 2.1729 0.0013 0.0271 0.8790 0.0360 − 0.0443 0.0072
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN 0.2854 0.6972 0.3356 0.3615 57.67 65.63 49.46
RW 0.3509 0.0025 − 0.0117 0.0142 47.62 48.96 46.24
B&S − 0.0259 0.1392 2.0566 − 2.0825 51.12 100.00 0.00
ARIMA 0.1363 − 0.2319 − 0.1289 − 0.1030 49.21 51.04 47.31
MLP 0.0875 − 0.5718 − 0.2988 − 0.2729 49.21 51.04 47.31
LSTM − 1.3067 − 1.2879 − 0.6569 − 0.6310 37.04 19.79 54.84
ARIMA+MLP − 0.7757 1.9676 0.9709 0.9967 68.25 57.29 79.57
ARIMA+LSTM 1.5317 0.6455 0.3098 0.3357 55.03 70.83 38.71
AdaBoost 0.1852 2.6144 1.2942 1.3201 75.13 82.29 67.74
LightGBM − 0.4340 2.3641 1.1691 1.1950 71.43 66.67 76.34
Simple RNN 0.5629 1.2358 0.6050 0.6308 61.38 67.71 54.84
GRU − 0.6326 0.2702 0.1222 0.1481 55.03 51.04 59.14

differently not only on different cryptocurrencies, but also in terms of performed best for Ripple and LightGBM showed superior performance
regression and investor statistics. As for the regression metrics, for Litecoin. For the pre-Covid-19 sub-period, the returns of the best
LightGBM and AdaBoost performed best for Bitcoin and Ethereum across performing methods ranged from 2.68 for Litecoin using AdaBoost to
the sub-periods studied. Different results were obtained for the two 4.93 for Ripple (Simple RNN). For the period following the emergence of
remaining cryptocurrencies with lower market capitalization. For Rip­ Covid-19, the returns ranged from 2.61 (for Bitcoin using AdaBoost) to
ple, LightGBM surpassed the remaining methods during the pre-Covid- 3.39 (for Litecoin using LightGBM). Exceptional MDA was obtained for
19 sub-period, while MLP and GRU outperformed the other methods all cryptocurrencies, ranging from 67.5% for Ethereum to 75.1% for
in the period following the emergence of Covid-19. Similarly, different Bitcoin. Generally, there was a greater MDA across cryptocurrencies
results are apparent for Litecoin, with the MLP and Simple RNN during the post-Covid-19 pandemic, resulting in improved predictability
demonstrating superior performance prior to and following the of cryptocurrency price trends. This is a rather remarkable result when
appearance of Covid-19, respectively. What is striking here is that, considering balanced performance achieved in all cases in terms of up­
except Bitcoin and Ethereum, these methods did not perform similarly ward and downward trend prediction. To compare the investor perfor­
well in terms of investor statistics, suggesting that although achieving mance statistically, we conducted a nonparametric Friedman test across
low forecast deviations, these methods failed to capture the direction of the investor metrics. The test uses the Friedman statistics to rank the
the next day's price change. Regarding the investor metrics, Simple RNN forecasting models across the two sub-periods. The Friedman p-value

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Table 5
Results of Ethereum forecasting performance – regression and investor metrics.
Before Covid-19 (2016-04-01 to 2019-12-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX

WN 9.1019 0.0026 0.0408 7.7331 0.0507 0.0279 − 0.0096

RW 6.4210 0.0032 0.0446 2.9206 0.0569 0.0019 − 0.0186
B&S – – – – – – –
ARIMA 3.3405 0.0018 0.0331 1.1155 0.0429 0.0584 0.0245
MLP 2.0626 0.0014 0.0276 0.5063 0.0371 0.4027 0.0192
LSTM 1.2799 0.0017 0.0301 1.0748 0.0406 − 0.0113 0.0818
ARIMA+MLP 3.5920 0.0015 0.0289 2.1820 0.0385 0.3814 0.0198
ARIMA+LSTM 3.0440 0.0017 0.0310 1.3090 0.0409 0.2626 0.0315
AdaBoost 3.2182 0.0012 0.0257 2.5112 0.0348 0.5126 0.0281
LightGBM 1.7602 0.0011 0.0237 1.3562 0.0334 0.5690 0.0441
Simple RNN 2.4482 0.0012 0.0260 1.4288 0.0347 0.5268 0.0016
GRU 2.1173 0.0012 0.0261 1.3738 0.0348 0.5225 − 0.0126
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN − 0.1181 0.3712 0.1729 0.1983 48.45 46.32 50.51
RW − 0.6564 0.2324 0.1035 0.1289 48.97 44.21 53.54
B&S − 0.0254 0.7985 2.8866 − 2.9119 52.11 100.00 0.00
ARIMA 0.7521 − 0.0252 − 0.0253 0.0001 48.45 49.47 47.47
MLP 0.2905 2.4304 1.2025 1.2279 62.89 64.21 61.62
LSTM − 0.8632 − 0.5598 − 0.2926 − 0.2672 47.94 48.42 47.47
ARIMA+MLP 0.7856 1.7765 0.8756 0.9009 57.22 58.95 55.56
ARIMA+LSTM 2.3276 0.9257 0.4502 0.4755 53.09 70.53 36.36
AdaBoost 0.6268 3.2507 1.6127 1.6380 64.43 66.32 62.63
LightGBM 0.6585 3.5207 1.7477 1.7730 67.53 70.53 64.65
Simple RNN 0.4325 3.5054 1.7400 1.7654 65.98 68.42 63.64
GRU 0.4298 3.3323 1.6535 1.6788 63.40 65.26 61.62

After Covid-19 (2020-01-01 to 2023-08-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX
WN 2.4354 0.0022 0.0350 0.6965 0.0465 0.0243 0.0841
RW 3.7473 0.0027 0.0410 − 0.1798 0.0522 0.1100 0.0203
B&S – – – – – – –
ARIMA 1.1594 0.0016 0.0287 0.7467 0.0397 0.0353 0.1312
MLP 1.6599 0.0011 0.0240 1.4470 0.0324 0.5900 0.0743
LSTM 1.1763 0.0016 0.0290 0.9329 0.0400 − 0.0930 0.1270
ARIMA+MLP 1.4629 0.0011 0.0250 1.0449 0.0336 0.5132 0.1086
ARIMA+LSTM 1.1498 0.0013 0.0266 0.5360 0.0366 0.3767 0.1312
AdaBoost 1.3491 0.0009 0.0230 1.1058 0.0294 0.6661 0.0497
LightGBM 1.4344 0.0009 0.0219 1.0440 0.0300 0.6437 0.1044
Simple RNN 2.0241 0.0019 0.0312 0.9193 0.0438 0.0566 0.0791
GRU 1.4885 0.0014 0.0277 1.1412 0.0380 0.2405 0.1175
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN − 0.0661 − 0.4673 − 0.2550 − 0.2124 43.39 48.51 37.50
RW − 0.5820 1.1031 0.5303 0.5729 56.08 50.50 62.50
B&S − 0.0426 0.4142 2.6858 − 2.7284 52.84 100.00 0.00
ARIMA 0.5349 − 0.1435 − 0.0930 − 0.0504 53.97 55.45 52.27
MLP − 1.3096 3.0747 1.5161 1.5586 67.72 52.48 85.23
LSTM − 1.1820 − 0.1093 − 0.0759 − 0.0333 51.85 44.55 60.23
ARIMA+MLP − 1.1435 2.5770 1.2672 1.3098 64.55 54.46 76.14
ARIMA+LSTM 1.9223 0.8068 0.3821 0.4247 60.32 72.28 46.59
AdaBoost − 0.6104 3.1822 1.5698 1.6124 66.67 62.38 71.59
LightGBM − 0.1119 3.3438 1.6506 1.6932 71.43 68.32 75.00
Simple RNN 0.0379 1.0002 0.4788 0.5214 56.08 55.45 56.82
GRU − 0.5029 1.1768 0.5671 0.6097 55.03 51.49 59.09

<0.01 (the Friedman statistics ranged from 35.3 to 56.2) indicates sig­ effective for some cryptocurrency time series. This finding is in contrast
nificant differences between the compared forecasting models for all the to recent review studies (Khedr et al., 2021; Ren et al., 2022), which
four cryptocurrencies. Among the forecasting models, the Simple RNN highlighted the dominance of LSTM models. This may be because con­
ranked first for Ripple, while LightGBM ranked first for Ethereum, Bit­ ventional models are just as effective as deep learning models, particu­
coin and Litecoin. larly when the data are univariate and there is no need to deal with
additional variables or complex relationships. Traditional computa­
5. Discussion tional models are based on statistical principles and assumptions that are
appropriate for univariate data, as these models take into account fac­
Overall, three different patterns were observed in our forecasting tors such as autocorrelation, seasonality and trend. Therefore, in the
results, with Bitcoin/Ethereum and Ripple/Litecoin representing these context of univariate time series analysis, where there are no additional
patterns. This finding is not surprising given the descriptive statistics of variables or complex relationships to consider, traditional quantitative
their time series. While the expected finding was that ensemble learning techniques can often be sufficient (Castán-Lascorz et al., 2022).
and deep learning methods outperform the conventional statistical We have shown that LSTM models can be overcome by GRU models,
methods and shallow neural networks, this study showed that, at least in even when LSTM is combined with ARIMA. One reasonable explanation
terms of point forecasts, less complex conventional models can be more for this decrease is that the ensemble learning and deep learning

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Table 6
Results of Ripple forecasting performance – regression and investor metrics.
Before Covid-19 (2016-04-01 to 2019-12-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX

WN 7.2913 0.0019 0.0342 − 2.3405 0.0441 0.0001 0.0637

RW 9.2486 0.0028 0.0421 − 4.3758 0.0527 − 0.0828 0.0299
B&S – – – – – – –
ARIMA 0.9997 0.0013 0.0255 0.9997 0.0358 0.0892 0.1486
MLP 1.5667 0.0014 0.0267 1.2493 0.0377 − 0.3116 0.1290
LSTM 1.8834 0.0013 0.0261 0.3450 0.0366 − 0.2481 0.1388
ARIMA+MLP 3.6238 0.0014 0.0278 2.5354 0.0368 0.1993 0.0868
ARIMA+LSTM 2.6338 0.0014 0.0293 0.8290 0.0380 0.1868 0.0908
AdaBoost 3.5384 0.0009 0.0220 2.7337 0.0305 0.5321 0.0829
LightGBM 2.8600 0.0008 0.0197 2.3387 0.0285 0.6182 0.1078
Simple RNN 3.6358 0.0027 0.0348 0.7220 0.0523 0.5112 0.1761
GRU 3.8229 0.0039 0.0447 1.7255 0.0627 0.1772 0.2071
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN 0.0156 0.0054 0.0048 0.0006 45.36 42.39 48.04
RW − 0.4854 − 0.2821 − 0.1390 − 0.1431 47.42 45.65 49.02
B&S 0.0041 0.9591 2.4816 − 2.4775 52.01 100.00 0.00
ARIMA − 4.7639 − 0.0265 − 0.0112 − 0.0153 52.58 1.09 99.02
MLP − 2.5181 − 1.5176 − 0.7567 − 0.7608 44.33 11.96 73.53
LSTM − 1.1531 − 1.5355 − 0.7657 − 0.7698 40.72 35.87 45.10
ARIMA+MLP 0.4418 0.7275 0.3658 0.3617 51.55 60.87 43.14
ARIMA+LSTM 2.0134 1.0897 0.5469 0.5428 52.06 72.83 33.33
AdaBoost 0.7292 3.2439 1.6240 1.6199 69.07 78.26 60.78
LightGBM 0.5372 3.4476 1.7258 1.7217 71.13 75.00 67.65
Simple RNN − 0.2844 4.9318 2.4881 2.4437 71.65 65.69 78.26
GRU − 0.2782 1.3665 0.7055 0.6610 54.12 51.96 56.52

After Covid-19 (2020-01-01 to 2023-08-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX
WN 5.5345 0.0040 0.0460 − 0.4069 0.0630 − 0.0075 0.0569
RW 7.0524 0.0054 0.0542 1.3672 0.0734 − 0.0037 0.0136
B&S – – – – – – –
ARIMA 0.9998 0.0027 0.0301 0.9998 0.0517 − 0.1947 0.1724
MLP 1.9275 0.0019 0.0262 1.0353 0.0440 0.5252 0.0052
LSTM 1.5035 0.0030 0.0321 1.1093 0.0545 − 0.4740 0.1443
ARIMA+MLP 2.4915 0.0032 0.0333 0.7799 0.0563 0.1655 0.0586
ARIMA+LSTM 2.5516 0.0035 0.0364 1.3587 0.0594 − 0.0738 0.1335
AdaBoost 1.1980 0.0022 0.0262 0.8145 0.0464 0.4479 0.1284
LightGBM 1.4219 0.0021 0.0252 0.7566 0.0459 0.4602 0.1004
Simple RNN 1.6898 0.0021 0.0267 0.6932 0.0457 0.4750 − 0.0053
GRU 1.4707 0.0020 0.0256 0.7454 0.0442 0.5184 0.0356
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN − 0.9814 0.7209 0.3550 0.3659 50.79 39.08 60.78
RW − 0.2337 − 0.1856 − 0.0982 − 0.0874 55.03 51.72 57.84
B&S − 0.0108 0.6931 2.8411 − 2.8520 53.52 100.00 0.00
ARIMA − 5.3480 − 0.3342 − 0.1725 − 0.1617 53.44 0.00 99.02
MLP 0.9483 2.5124 1.2508 1.2616 66.67 81.61 53.92
LSTM 1.9768 − 1.8340 − 0.9224 − 0.9116 41.27 78.16 9.80
ARIMA+MLP 0.2686 1.6379 0.8135 0.8244 59.26 58.62 59.80
ARIMA+LSTM 2.5810 − 1.2910 − 0.6509 − 0.6401 45.50 67.82 26.47
AdaBoost 1.0692 2.3798 1.1845 1.1953 66.67 82.76 52.94
LightGBM 0.6917 2.9912 1.4902 1.5010 72.49 77.01 68.63
Simple RNN 0.3032 2.7200 1.3546 1.3654 69.31 71.26 67.65
GRU 0.5134 2.7135 1.3513 1.3621 69.84 74.71 65.69

methods were overfitted for the less complex time series. The poor inefficient cryptocurrency markets, whereas Bitcoin appears to be the
performance of the hybrid models might be due to the fact that there is a least inefficient market. This complexity effect might also be related to
lot of noise in the residuals, so the hybrid models get overfitted by the greater liquidity in the Bitcoin market (Al-Yahyaee et al., 2020).
noise. Our results indicate that the trading strategies based on deep
Different results were observed for the investor metrics, suggesting learning (for Ripple) or ensemble learning (for Bitcoin, Ethereum, and
that more complex machine learning methods are needed to adequately Litecoin) could allow cryptocurrency investors to effectively predict
perform in terms of forecasting cryptocurrency market direction. We market development, particularly in less complex cryptocurrency mar­
have shown that remarkable returns can be achieved by following the kets. The study's findings provide cryptocurrency investors with valu­
trading strategy based on the forecasts produced by the LightGBM able insights into effective trading strategies, adjusting their investment
models. This remarkable performance can be attributed to effectively strategy to either take a long position or a short position. The demon­
managing large datasets while exploiting its regularization mechanism strated financial effectiveness of deep and ensemble learning techniques
that helps prevent overfitting, making it more robust for cryptocurrency in cryptocurrency trading also offers new tools for financial analysts,
price forecasting (Sun et al., 2020). The highest returns could be ob­ enhancing their ability to predict market movements. Nonetheless,
tained for Ripple in the pre-Covid-19 period and for Litecoin in the post- policymakers ought to implement financial market interventions with a
Covid-19 period, indicating that these cryptocurrencies are the most view to enhancing the level of transparency and efficiency in these

9
A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

Table 7
Results of Litecoin forecasting performance – regression and investor metrics.
Before Covid-19 (2016-04-01 to 2019-12-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX

WN 12.7863 0.0035 0.0432 4.6522 0.0592 0.0114 0.1668

RW 13.6119 0.0042 0.0494 − 2.8895 0.0651 0.0034 0.1641
B&S – – – – – – –
ARIMA 1.0051 0.0020 0.0235 0.9942 0.0444 − 0.0340 0.2863
MLP 2.2688 0.0012 0.0196 ¡0.0703 0.0351 0.6398 0.2427
LSTM 1.2487 0.0021 0.0243 0.8344 0.0458 − 0.2085 0.2534
ARIMA+MLP 4.9575 0.0018 0.0266 1.8160 0.0428 0.3245 0.2269
ARIMA+LSTM 3.6209 0.0018 0.0257 1.3296 0.0424 0.3529 0.2300
AdaBoost 3.1387 0.0015 0.0216 0.2177 0.0386 0.5106 0.2526
LightGBM 2.4554 0.0014 0.0196 − 0.1327 0.0371 0.5663 0.2406
Simple RNN 2.5022 0.0014 0.0222 − 0.2846 0.0379 0.5342 0.2245
GRU 2.8096 0.0014 0.0217 − 0.3606 0.0369 0.5598 0.2114
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN − 0.6098 0.1510 0.0696 0.0814 49.48 46.46 52.63
RW 0.0433 0.3973 0.1927 0.2045 53.09 51.52 54.74
B&S − 0.0118 0.5278 2.2580 − 2.2698 50.29 100.00 0.00
ARIMA 3.6668 0.0241 0.0062 0.0179 51.03 95.96 4.21
MLP 0.1161 2.5623 1.2752 1.2870 67.01 66.67 67.37
LSTM − 1.7866 − 1.2000 − 0.6059 − 0.5941 47.42 29.29 66.32
ARIMA+MLP − 0.0941 2.5942 1.2912 1.3030 60.31 52.53 68.42
ARIMA+LSTM 2.7781 0.4407 0.2145 0.2263 56.70 70.71 42.11
AdaBoost − 0.2214 2.6827 1.3354 1.3472 66.49 54.55 78.95
LightGBM − 0.2178 2.6739 1.3311 1.3428 68.04 63.64 72.63
Simple RNN − 0.3447 2.2188 1.1035 1.1153 64.95 62.63 67.37
GRU − 0.1891 2.4517 1.2200 1.2317 65.98 65.66 66.32

After Covid-19 (2020-01-01 to 2023-08-31)

Method MAPE ME MAE MPE RMSE R MIN-MAX
WN 5.3427 0.0031 0.0397 3.2827 0.0557 − 0.1341 0.1282
RW 14.4445 0.0036 0.0459 − 8.4577 0.0604 0.0856 0.1208
B&S – – – – – – –
ARIMA 0.9989 0.0020 0.0290 0.9989 0.0444 0.0633 0.2086
MLP 2.6556 0.0016 0.0277 0.4133 0.0403 0.4409 0.1507
LSTM 1.5458 0.0021 0.0298 1.3016 0.0453 − 0.0191 0.1783
ARIMA+MLP 1.2830 0.0012 0.0274 0.9887 0.0347 − 0.5306 0.0890
ARIMA+LSTM 1.1576 0.0011 0.0263 0.8930 0.0333 0.5702 0.0972
AdaBoost 2.9554 0.0010 0.0229 1.1805 0.0319 0.6975 0.0000
LightGBM 3.4677 0.0012 0.0224 1.4952 0.0353 0.6198 0.1566
Simple RNN 2.2888 0.0008 0.0216 1.0384 0.0287 0.5444 0.0120
GRU 2.2607 0.0018 0.0278 0.4635 0.0425 0.3090 0.1680
Method SP Return Return_long Return_short MDA[%] MDAþ[%] MDA-[%]
WN − 0.5277 − 0.3957 − 0.1953 − 0.2005 47.09 43.62 50.53
RW − 0.0799 0.9031 0.4542 0.4490 52.91 57.45 48.42
B&S 0.0052 0.5019 2.7536 − 2.7484 51.36 100.00 0.00
ARIMA 5.2291 0.2005 0.1028 0.0976 50.26 97.87 3.16
MLP − 0.5707 2.0535 1.0293 1.0241 58.73 54.26 63.16
LSTM 0.4309 − 0.8283 0.4116 0.4168 48.15 50.00 46.32
ARIMA+MLP 1.1153 2.6573 1.3402 1.3171 48.04 52.50 44.09
ARIMA+LSTM 2.0505 0.9450 − 0.4840 − 0.4610 41.27 15.63 67.74
AdaBoost 0.7442 2.9949 1.5000 1.4948 66.14 78.72 53.68
LightGBM 0.3632 3.3869 1.6960 1.6908 74.60 76.60 72.63
Simple RNN 0.3974 2.6986 1.3552 1.3435 68.25 74.19 62.50
GRU − 0.7234 1.5542 0.7797 0.7745 63.49 57.45 69.47

markets. According to our findings on the predictability of crypto­ 6. Conclusion

currency price trends, this seems particularly important in the post-
pandemic period. In this study, we have provided a comparative study of univariate
Given the study design, caution must be exercised when interpreting ensemble learning and deep learning models for forecasting crypto­
the results, as the second sub-period period included the Covid-19 currency prices. We have conducted extensive experiments using his­
pandemic period, which positively affected cryptocurrency market ef­ torical time-series data from four major cryptocurrencies. For the
ficiency (Mnif et al., 2020), as well as its role as a store of value (Corbet regression results, the results show the higher effectiveness of complex
et al., 2020). Although we used the most recent data available, more machine learning methods for all four cryptocurrency time series. More
research is needed to validate our findings for the post-pandemic data. importantly, we investigated the efficacy of trading strategies based on
This study also failed to account for the portfolio returns, suggesting that forecasting models, showing that LightGBM may provide highly profit­
future studies should focus on the construction of trading strategies for able trading strategies for investors in the Bitcoin, Ethereum and Lite­
portfolio investors. coin markets. For the Ripple market, Simple RNN is recommended as the
best forecasting model for investors. Strikingly, these findings appear to
be robust to the sub-periods studied. Taken together, these findings
suggest that ensemble learning and deep learning models can effectively

10
A. Bouteska et al. International Review of Financial Analysis 92 (2024) 103055

guide investors in their trading decisions. In the future, we will examine Derbentsev, V., Matviychuk, A., & Soloviev, V. N. (2020). Forecasting of cryptocurrency
prices using machine learning. In Advanced Studies of Financial Technologies and
more frequent real-time data to better exploit the advantages of deep
Cryptocurrency Markets (pp. 211–231).
learning models. In a similar manner, we seek to utilize multivariate Dong, F., Xu, Z., & Zhang, Y. (2022). Bubbly bitcoin. Economic Theory, 74(3), 9731015.
data, including the determinants of cryptocurrency supply and demand, Efat, M. I. A., Petr, H., Abedin, M. Z., Azad, R. U., Jaber, M. A., Aditya, S., & Hassan, M. K.
in order to compare the performance of univariate and multivariate (2022). Deep learning model using hybrid adaptive trend estimated series for
modelling and forecasting sales. Annals of Operations Research. https://doi.org/
models. In this way, we would also be able to interpret the models more 10.1007/s10479-022-04838-6
effectively in terms of the contribution of the determinants. El Montasser, G., Charfeddine, L., & Benhamed, A. (2022). COVID-19, cryptocurrencies
bubbles and digital market efficiency: Sensitivity and similarity analysis. Finance
Research Letters, 46, Article 102362.
Data availability Fakhfekh, M., & Jeribi, A. (2020). Volatility dynamics of crypto-currencies’ returns:
Evidence from asymmetric and long memory GARCH models. Research in
Data will be made available on request. International Business and Finance, 51, Article 101075.
Fang, T., Su, Z., & Yin, L. (2020). Economic fundamentals or investor perceptions? The
role of uncertainty in predicting long-term cryptocurrency volatility. International
Acknowledgements Review of Financial Analysis, 71, Article 101566.
Fu, E., Zhang, Y., Yang, F., & Wang, S. (2022). Temporal self-attention-based ConvLSTM
network for multivariate time series prediction. Neurocomputing, 501, 162–173.
This research paper was made possible by a grant from the Czech Fuss, R., & Koller, J. (2016). The role of spatial and temporal structure for residential rent
Sciences Foundation (No. 22-22586S). predictions. International Journal of Forecasting, 32(4), 1352–1368.
Guesmi, K., Saadi, S., Abid, I., & Ftiti, Z. (2019). Portfolio diversification with virtual
currency: Evidence from bitcoin. International Review of Financial Analysis, 63, Article
Appendix A. Supplementary data
431437.
Hajek, P., Hikkerova, L., & Sahut, J. M. (2023). How well do investor sentiment and
Supplementary data to this article can be found online at https://doi. ensemble learning predict bitcoin prices? Research in International Business and
org/10.1016/j.irfa.2023.103055. Finance, 64, Article 101836.
Hansun, S., Wicaksana, A., & Khaliq, A. Q. (2022). Multivariate cryptocurrency
prediction: Comparative analysis of three recurrent neural networks approaches.
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