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Annals of Science and
Technology
-
C,
Vol 6 (2):
47
-
56
, 2021
Copyright: An Official
Journal
of the Nigerian Young Academy
ISSN: 2 544 6320
ARTICLE
This journal is © The Nigerian Young Academy 2021
Annals of Science and
Technology
2021
Vol. 6
(2)
47
-
56
|
47
Price Analysis and Forecasting for Bitcoin Using Auto Regressive
Integrated Moving Average Model
Olufunke G. Darley
,*
, Abayomi I. O. Yussuff, Adetokunbo A. Adenowo
Electronic & Computer Engineering Department, Lagos State University, Nigeria.
Received 3
rd
September, 2021, Accepted 9
th
November, 2021
DOI: 10.2478/ast-2021-0009
*Corresponding author
Olufunke G. Darley E-mail: funke_darley@yahoo.com
Tel: +234- 8023065513
Abstract
This paper investigated Bitcoin daily closing price using time series approach to predict future values for financial
managers and investors. Daily data were sourced from CoinDesk, with Bitcoin Price Index (BPI) for 5 years (January
1, 2016 to May 31, 2021) extracted. Data analysis and modelling of price trend using Autoregressive Integrated
Moving Average (ARIMA) model was carried out, and a suitable model for forecasting was proposed. Results showed
that ARIMA(6,1,12) model was the most suitable based on a combination of number of significant coefficients and
values of volatility, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). A two-month test
window was used for forecasting and prediction. Results showed a decline in prediction accuracy as number of days
of the test period increased; from 99.94% for the first 7 days, to 99.59 % for 14 days and 95.84% for 30 days. For
the two-month test period, percentage accuracy was 84.75%. The study confirms that the ARIMA model is a
veritable planning tool for financial managers, investors and other stakeholders; especially for short-term
forecasting. It is however imperative that the influence of external factors, such as investors’/influencers’ comments
and government intervention, that may affect forecasting be taken into consideration.
Keywords: ARIMA Model, Bitcoin Forecast, Short-term Prediction, Time Series
©2021 Darley et al.
This work is licensed under the Creative Commons Attri bution-Non-Commercial-NoDerivs License 4.0
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The Nigerian Young Academy 2021
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2021
Vol. 6
(2)
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1.0 Introduction
Rapid advancement in digital technology and increasing capacity of
computer systems (in terms of speed and data storage) has created an
opportunity for Digital Signal Processing (DSP) techniques in
engineering to be applied to the finance industry. One of the
applications of DSP in Finance is in prediction of future market value
of a business, through the use of historical financial data whose
quantity is usually massive and requires absolute objectivity in its
calculations (Nepal, 2015). Thus, financial managers can make
decisions based on statistical analysis of financial time series and the
modeling of its behavior; the aim being to perform predictions and
systematically optimize investment strategies which has become
fundamental to successful investments (Feng and Palomar, 2016).
Bitcoin (BTC) is the world's largest cryptocurrency and its emergence
as a veritable digital currency which has captured global attention, in
just over a decade, has been unexpected. It is a form of peer-to-peer
electronic cash system, without the need to reveal one’s identity for a
transaction to happen and without a middle man (Nakamoto, 2008).
Despite its modest beginning in 2009 when it was launched at $1.00
value, it has grown into tens of thousands of dollars in value. It is
measured by market capitalization and amount of data stored on its
blockchain (Shen et al, 2018) and it offers lower transaction fees than
traditional online payment mechanisms.
As with all businesses and trades, the COVID-19 pandemic has had an
impact on trading of Bitcoin and its price. On March 11, 2020, the
World Health Organization (WHO) declared COVID-19, a disease
caused by a strain of Coronavirus, a global pandemic (Ghebreyesus,
2020). Data from CoinDesk (Coindesk, 2021), an Organization
involved in the monitoring and publishing of Bitcoin data was used to
observe Bitcoin price behaviour, before and during the pandemic.
Bitcoin price index from January 2016 to May 2021 is shown in Figure
1.
It was observed that the increase in price of Bitcoin was gradual from
inception to the beginning of 2017 when its price was about $1,000.00.
From then, it witnessed steady increases until December 2017 when it
increased sharply and peaked at $19,116.979 unit price on December
17, 2017. Thereafter, the price witnessed a decline to minima of
$3,952.448 on November 30, 2018 but reversed the downward
movement and increased steadily to $5,800.209 on March 13, 2020
(two days after declaration of the pandemic). Despite the pandemic, it
was observed that the price of Bitcoin experienced a steep incline and
peaked at $57,128.643 on February 22, 2021. This is an increase of
almost 1000% within a year. On the one-year anniversary of COVID-
19, being March 11, 2021, the closing price of Bitcoin was $56,915.170.
Figure 1: Bitcoin Daily Closing Price Time Series from January 2016 to
May 2021
The increased interest in Bitcoin and the subsequent price surge can
be attributed to investors using it as hedge, being protection against
financial loss, (Demir et al, 2020) due to uncertainties raised by the
pandemic; and the subsequent national restrictions and lockdowns
which led to the suppression of major world economies and global
recession. Other factors (CNBC, 2021; Tepper, 2021) that
coincidentally contributed to the rise of Bitcoin price during the period
include:
i. Institutional Adoption of Cryptocurrencies
Increasing adoption of cryptocurrencies by some traditional financial
institutions (e.g., BNY Mellon, Fidelity, Mastercard) which was seen as
an acknowledgement of the future viability of digital assets.
ii. Halving of Bitcoin
‘Halving’ (Masters, 2019) of Bitcoin in May 2020 which is an event that
happens every four years when the reward that bitcoin “miners”
receive for mining gets cut in half as a built-in mechanism to slow the
creation of new bitcoins and limit bitcoin’s supply. It is an event that
reminds investors of bitcoin’s scarcity thus leading to increased
demand.
iii. Adjustment of View
Revision of criticism and softening of views of major Wall Street
investors/players about cryptocurrencies.
iv. Acceptance by Major Payment Platforms
Acceptance of cryptocurrencies by major payment platforms (PayPal
and Square) with its announcement that it will soon allow buying,
holding, and trading of bitcoin and other cryptocurrencies, on its
platform which has contributed to the surge.
v. Pandemic-related Stimulus Programs
Stimulus programs by governments around the world have created
fear of inflation with investors looking for alternative assets to invest
200 400 600 800 1000 1200 1400 1600 1800
Index
0
1
2
3
4
5
6
7
Daily Closing Price (USD)
10
4
BitcoinTime Series Plot (Jan. 2016 - May 2021)
ClosingPri ceUSD
Darley et al., 2021 Price Analysis and Forecasting for Bitcoin
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in, thereby leading to high demand for Bitcoin. It is believed that
government monetary aid strengthens the appeal of Bitcoin.
However, by middle of May 2021, there was a dramatic drop in Bitcoin
price and this continues till date. The rapid growth in Bitcoin price and
its volatility continues to pique the interest of researchers (Demir et al,
2020; Amjad and Shah, 2017; Roche and McNally, 2018; Jang and Lee,
2018; Baur and Dimpfl, 2020; Fauzi et al, 2020).
Various methods have been developed and applied in time series
analysis. These include ARIMA model (Box and Jenkins, 1976;
Brockwell and Davis, 2002) which uses the current value of the
stationary time series based on its values at previous times and errors
in values at previous time periods; Artificial Neural Network (ANN)
model, which has the ability to learn patterns from time series data and
uses these to model the problem and deduce solutions (Zamani et al,
2012; Selvamuthu et al, 2019) and hybrid models which combine the
strengths of the ARIMA and ANN models (Merh et al, 2010; Wang, et
al, 2012). While models based on neural networks have been found to
present higher accuracy in some cases, the ARIMA model is selected
for its robustness, simplicity, ease of application and high accuracy for
short term forecasting.
The Auto Regressive Integrated Moving Average (ARIMA) model, also
known as the Box-Jenkins methodology (Box and Jenkins, 1976;
Brockwell and Davis, 2002) in financial analysis, was used in analyzing
Bitcoin time series data and forecasting. The ARIMA model is a
combination of the autoregressive (AR) model and the moving average
(MA) model with the stationarity (differencing or integration) of the
time series taken into account. Stationarity (Feng and Palomar, 2016)
is an important characteristic for time series analysis which describes
the time-invariant behavior of a time series and is much easier to
model, estimate, and analyze. Stationarity of a time series is a major
assumption in ARIMA modeling and since market prices by nature are
non-stationary, stationarity must be ensured by differencing the time
series (Brockwell and Davis, 2002) before forecasting can be done. The
ARIMA model is simple but nonetheless powerful and it aims to
describe autocorrelations in time series data (Brockwell and Davis,
2002; Ariyo et al, 2014). Essentially, the future value of a variable is
based on a linear combination of past values of observation (lags) and
past errors. Lags are very useful in time series analysis because they
indicate the tendency for values to be correlated with previous copies
of itself. The ARIMA model can be represented as ARIMA(,, ) model
in Equation (1) or ARIMA(,, ) model in Equation (2) respectively.
= + ∑
+
+∑
(1)
where
is actual value at t
is the random error at t
is a constant
is the observation coefficients
are error coefficients
are integers
is the number of lags of observation
is the number of lags of error term
∆
= + ∅
∆
+ ⋯ + ∅
∆
+
+
+ ⋯ +
(2)
where
∆
denotes a
differenced time series
number of time series was differenced to obtain stationarity
is a constant
is an uncorrelated innovation process with mean zero (error).
and
are coefficients of observation and error lags respectively
is the number of lags of observation
is the number of lags of error term
Prediction accuracy, as represented by the Mean Absolute Percentage
Error (MAPE), compares predicted values from the ARIMA model and
actual values from the time series as shown in Equation (3).
= 1 −
||
100% (3)
In this paper, Bitcoin daily closing price time series spanning January
2016 to May 2021 (as represented graphically in Figure 1) was
analyzed using MATLAB (R2018a); and forecasts made. This is of
particular importance due to the popularity of Bitcoin and volatility of
its price. Forecast values can be useful to investors in developing
profitable trading strategies. For government regulators and policy
makers, it helps to formulate appropriate policies. Overall, it assists
relevant stakeholders to take informed decisions.
2.0 Experimental
In this section, the methodology used for this work is described. This
includes steps such as data collection and data analysis.
Data Collection
Bitcoin daily closing price time series data from Jan 2016 to May 2021
(as represented in Figure 1) was obtained from (Coindesk, 2021). The
Bitcoin data comprises four variables: Closing Price, 24h Open, 24h
High and 24h Low; all in USD. The daily closing price (USD) was chosen
to represent the price of the index to be predicted since it reflects all
the activities of the index on a trading day.
Data Analysis
To determine a suitable model, the following steps as described in
subsequent paragraphs, were carried out on Bitcoin price time series:
1. Series inspection for determination of stationarity
2. Differencing to ensure stationarity
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3. Modeling through the 4-step process of
i) Model Identification
ii) Parameter Estimation
iii) Diagnostics
iv) Forecasting
Inspection of the time series must confirm if it is stationary or
otherwise. This is done by visual inspection and plots of the partial
autocorrelation function (PACF) and the autocorrelation function
(ACF) of the series which is a measure of the relationship between a
variable’s current value and its past values. Auto correlation
summarizes the relationship between the values of the same series at
previous times and its plot by lag is called the auto correlation function
ACF. Partial autocorrelations summarizes the relationship between an
observation at prior time steps with the relationships of intervening
observations removed and its plot by lag is called partial
autocorrelation function, PACF (Brockwell and Davis, 2002).
Stationarity is further confirmed by the Augmented Dickey-Fuller test
which is based on a null hypothesis that there is a unit root in the data
(Brockwell and Davis, 2002). In general, a probability value (p-value)
of less than 5% indicates rejection of the null hypothesis and proves
stationarity while a p-value of greater than 5% indicates acceptance of
the hypothesis and hence non-stationarity. Non-stationary data as a
rule can be unpredictable and therefore cannot be modelled or
forecasted. It must be converted through the process of differencing
which can be said to be the number of times that raw observations are
differenced. If a time series is made stationary, any model that is
inferred from it can be taken to be stationary, therefore providing a
valid basis for forecasting (Al-Shiab, 2006).
Model identification involves using the ACF and the PACF (as explained
above) of the differenced time series to plot correlograms from which
coefficients (,) which give the best fitting are determined. The
number of times the time series was differenced to ensure stationarity,
(Brockwell and Davis, 2002) is also taken into consideration. Hence
the coefficients (,, ) are determined.
Parameter estimation involves determining the number of significant
coefficients in the model that is being considered, volatility (variance)
values, Akaike Information Criterion (AIC) value, Bayesian
Information Criterion (BIC) value and the Ljung-Box test value. The
AIC is an estimator of prediction error and evaluates how well a model
fits the data it was generated from and the relative amount of
information lost; the less the loss, the higher the quality of the model.
The Bayesian Information Criterion is another criterion for model
selection among a finite set of models. The model with the lowest value
of AIC, BIC and volatility is considered the most suitable (Anderson,
2008). The Ljung-Box test is also a unit root test.
Model diagnostics involves running residual ACF to ensure that all
time series data is captured by the selected model. This is indicated by
all coefficients being within the significance bounds. If this is not the
case, parameters must be re-estimated. However, in re-estimating,
parsimony must be taken into consideration. This is because
parsimonious models give better forecasts than over-parameterized
models. Thus, in choosing the most suitable ARIMA model, it is
important to keep parsimony in view.
When the model has been confirmed as suitable with the best
coefficients, forecasting of future prices of Bitcoin from April 2021 to
May 2021 was done using MATLAB Econometrics Tool and was
validated by plotting forecasted values against actual series for
comparison. Prediction accuracy (MAPE) was also plotted.
3.0 Results
By visual inspection (Figure 1), the Bitcoin closing price time series is
not stationary. Non-stationarity is further confirmed by the sharp
drop-off of the Partial Autocorrelation Function (PACF) plot at lag 1
(Figure 2a) and the very slow decline of the Autocorrelation Function
(ACF) plot (Figure 2b).
The Augmented Dickey-Fuller (ADF) test (Table 1) is applied to the
Bitcoin daily closing price time series and it can be observed that the
ADF did not reject the null hypothesis and has a p-value of 0.7756
which is greater than the significance level value of 0.05; thus
indicating non-stationarity. Therefore, it is necessary to difference the
series to obtain stationarity (Brockwell and Davis, 2012).
The differenced time series (Figure 3) confirms stationarity by having
constant mean and variance around zero, the PACF (Figure 4a) and the
ACF (Figure 4b) being similar and the ADF unit root test (Table 2)
accepting the null hypothesis with a p-value of 1.0000e-03 which is
less than the significance level value of 0.05. All these indicate
stationarity. Therefore, series became stationary with first difference.
Figure 3: Differenced Time Series for Bitcoin Daily Closing Price (USD)
With stationarity confirmed, the process for ARIMA modelling of the
Bitcoin daily closing price time series was carried out. The following
likely models were identified and investigated: ARIMA(2,1,2),
ARIMA(2,1,3), ARIMA(2,1,6), ARIMA(3,1,2), ARIMA(3,1,3),
ARIMA(3,1,6), ARIMA(6,1,2), ARIMA(6,1,3) and ARIMA(6,1,6). Each
model had its parameter values and goodness of fit determined using
the combination of number of significant coefficients, volatility, Akaike
Information Criteria (AIC) and Bayesian Information Criterion (BIC)
values. See Table 3. As a starting point, ARIMA(6,1,6) was conditionally
selected based on highest number of significant coefficients and lowest
values of volatility and AIC; but must be confirmed by running residual
diagnostics to ensure that all its coefficients are within the significance
interval.
Running Residual ACF (Figure 5a) on ARIMA(6,1,6) showed that there
were outliers at lags 10, 12 and 14 which indicates that not all
information of the time series has been captured in the model and
there was therefore a need for model re-estimation. Re-estimation
involved taking the outliers mentioned above into consideration and
re-running residual diagnostics. ARIMA(6,1,12) model was found to
present a better performance and its residual diagnostics showed that
it has all coefficients located within the confidence interval (Figure 5b).
In addition, it has lowest values of volatility and AIC (Table 3). Thus, of
Darley et al., 2021 Price Analysis and Forecasting for Bitcoin
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all the models considered, ARIMA (6,1,12) is the most appropriate
model for this time series.
The Ljung-Box test for residual correlation, squared residual ACF
(Figure 6) shows all coefficients outside the 95% confidence interval
signifying that there is no correlation between the coefficients and
thus ARIMA(6,1,12) is a good model for forecasting.
Table 4 shows actual versus forecast values for Bitcoin daily closing
price in April 2021 from which prediction accuracy (MAPE) was
derived. It can be observed that ARIMA(6,1,12) gives very close
forecast values for the first seven days (April 1-7, 2021), with a
prediction accuracy of 99.94%. Prediction accuracy however
decreases for longer forecast periods; dropping to 99.59% for 14 days
forecast (April 1-14) and 95.84% for 30 days (April 1-30) forecast
period. These are all considered good results; being above 95%
accuracy. In other words, close predictions resulting in higher
accuracy values were obtained for shorter prediction periods. This
was the case until after April 18 when a significant dip was
experienced and was subsequently followed by a continuous decline.
In addition, forecast for a two-month (April-May 2021) window period
(Figure 7a) and the prediction accuracy (Figure 7b) were presented. It
was observed that as number of forecast days increased, MAPE
decreased; having a value of 84.75% at the end of the period. This
confirmed that ARIMA modelling is better suited for short-term
predictions and less so for longer-terms.
Bitcoin daily closing price time series with forecast values for April –
May, 2021 and April – June, 2021, respectively, are shown in Figures
8a and 8b. The model for the selected time periods predicted an
upward movement of Bitcoin price. This is in agreement with
predictions of some market analysts (McGlone, 2021; Bambysheva et
al, 2021; White, 2021). A series of events in May 2021, however, led to
an unexpected decline in the fortunes of Bitcoin. Specifically, Bitcoin
plummeted to nearly $30k after reaching a record high of more than
$64k in April 2021. This can be ascribed to external factors which have
been broadly categorized as follows:
1. Influencers’ Comments
Comments of influential persons/investors that directly impact prices.
For example, the tweet of Elon Musk on May 12, 2021 in which he said
Tesla will no longer accept Bitcoin as payment method due to concerns
over its energy usage, leading to loss of billions of dollars in value of
the crypto market. Another tweet on June 4, 2021, suggesting
‘breakup’ with Bitcoin led to a 4.3% decline in price. (Browne, 2021).
2. Government Intervention:
For instance, Chinese Government’s ban on May 18, 2021 whereby
domestic banks and financial institutions were forbidden from
supporting Bitcoin mining and transactions due to energy and money
laundering concerns (BBC, 2021; CBS, 2021).
3. Other influences
Bitcoin price fluctuations occurred for various other reasons including
but not limited to media coverage, actions of Speculators and
availability of Bitcoin.
While these factors would have been mostly reflected in the historical
data, not all influences can be captured and due to unforeseen events,
this can lead to variances between forecasted and actual values of
Bitcoin. This highlights the importance of including external factors
into forecast models.
Table 1: ADF Test for Bitcoin Daily Closing Price (USD) Time Series
Null Rejected P-Value Lags Model Significance Level
False 0.7117 20 AR 0.0500
Table 2: ADF Test for Bitcoin Daily Closing Price (USD) Differenced
Time Series
Null Rejected P-Value Lags Model Significance Level
True 1.0000e-03 20 AR 0.0500
Figures 2a &2b: PACF and ACF Plots for Bitcoin Closing Price (USD)
Darley et al., 2021 Price Analysis and Forecasting for Bitcoin
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Figure 3: Differenced Time Series for Bitcoin Daily Closing Price (USD)
Figures 4a & 4b: PACF and ACF for Differenced Time Series for Bitcoin Daily Closing Price (USD)
Table 3: Summary of Parameter Values and Goodness of Fit for selected ARIMA Models
ARIMA Model
No. of Significant Coefficients Volatility
AIC
BIC
2,1,2 0 4.4366e+05 3.0604e+04 3.0637e+04
2,1,3 0 4.3773e+05 3.0605e+04 3.0644e+04
2,1,6 4 4.3595e+05 3.0556e+04 3.0612e+04
3,1,2 1 4.4015e+05 3.0605e+04 3.0644e+04
3,1,3 0 4.3773e+05 3.0589e+04 3.0633e+04
3,1,6 0 4.3918e+05 3.0552e+04 3.0613e+04
6,1,2 1 4.3569e+05 3.0580e+04 3.0635e+04
6,1,3 1 4.5290e+05 3.0557e+04 3.0618e+04
6,1,6 2 4.3405e+05 3.0549e+04 3.0627e+04
6,1,12 2 4.2559e+05 3.0530e+04 3.0642e+04
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Figures 5a &5b: Residual ACF for ARIMA (6,1,6) and ARIMA (6,1,12)
Figure 6: Ljung-Box Test for Residual Correlation for ARIMA (6,1,12)
Figures 7a&7b: Actual vs. Forecast Values and Percentage Accuracy of Forecast for April-May 2021
Darley et al., 2021 Price Analysis and Forecasting for Bitcoin
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Figures 8a&8b: Bitcoin Closing Price Daily Forecast for April - May 2021 and April - June 2021
Table 4: Actual vs. Forecast Values for Bitcoin Daily Closing Price in April 2021
No. of Days Actual Forecast MAPE
(%)
No. of
Days Actual Forecast MAPE (%)
1 58724.66 58730.98 99.99
16 63346.79 59660.17 94.18
2 58984.61 58198.74 98.67
17 61965.78 60126.36 97.03
3 58821.63 58160.76 98.88
18 60574.44 60330.64 99.60
4 57517.80 57643.05 99.78
19 56850.83 60282.30 93.96
5 58177.40 57935.72 99.58
20 56224.10 60088.34 93.13
6 58843.56 58550.25 99.50
21 56608.77 59823.50 94.32
7 58040.19 59657.93 97.21
22 54144.43 59562.04 89.99
8 56508.94 60220.96 93.43
23 51965.06 59432.92 85.63
9 57880.91 60482.49 95.51
24 50669.14 59541.48 82.49
10 58171.91 60298.44 96.34
25 50733.77 59842.06 82.05
11 59295.95 59935.85 98.92
26 48542.95 60155.82 76.08
12 59822.90 59469.11 99.41
27 53558.71 60329.31 87.36
13 59853.20 59043.19 98.65
28 55123.86 60339.59 90.54
14 63223.88 58890.09 93.15
29 54591.52 60246.10 89.64
15 62926.56 59141.65 93.99
30 53260.30 60101.59 87.15
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Conclusion
Rapid advancement in digital technology has created an opportunity
for DSP techniques in engineering to be applied to the Finance
industry; such as price forecast of financial products using financial
time series. Various methods have been developed and applied in time
series analysis which include ARIMA, ANN and Hybrid models which
combine the strengths of the ARIMA and ANN models. While models
based on neural networks have been found to present higher accuracy
in some cases, the ARIMA model is selected for its robustness,
simplicity, ease of application and high accuracy for short term
forecasting.
In this paper, we have conducted the forecast of Bitcoin daily closing
price using the ARIMA model in order to assist investors in their
investment decisions. This is because price forecast of Bitcoin
constantly attracts attention due to its direct monetary advantage.
MATLAB was used for model identification, parameter estimation,
diagnostics and forecasting and ARIMA (6,1,12) model was selected as
the most suitable based on number of significant coefficients, values of
volatility, AIC and BIC, and having all coefficients within the
significance interval for residual diagnostics. Prediction accuracy or
mean absolute percentage error (MAPE) was obtained for a two-
month (April-May 2021) test window. ARIMA (6,1,12) model gave
very close forecast values for the first seven days of forecast (April 1-
7, 2021) with a prediction accuracy of 99.94%. This however
decreased for longer forecast periods; dropping to 99.59% for 14 days
forecast period (April 1-14) and 95.84% for 30 days (April 1-30)
forecast period. Despite the reduction, these are considered good
results; being above 95% accuracy. Thus, this reinforces the ease of
application and suitability of ARIMA models for short - term forecast
only; as against more complex models such as artificial neural network
models. The study confirms that the effect of the global pandemic on
Bitcoin price was positive with surge in its value which can be
attributed to investors using it as hedge against uncertainties raised
by the pandemic and the subsequent national restrictions and
lockdowns which led to the suppression of major world economies and
global recession. The time series for Bitcoin prices with forecasted
values showed an upward trend of daily closing price but this is
contrary to actual market value. This variance can be attributed to the
effect of external factors on Bitcoin prices such as tweets/comments of
influential persons (e.g. Elon Musk), government intervention (e.g.
China’s ban on institutional support for Bitcoin mining and
transactions) and other factors (e.g. media coverage and activities of
speculators) which all combined to weaken prediction.
In conclusion, even though the ARIMA model has been shown to
present efficient capability in generating short-term forecasts; other
external factors and influences as stated above must also be taken into
consideration for a more robust forecast.
Declaration of Conflict of Interests
All authors have declared that there are no conflicts of interests.
Authors’ Contributions
Conception: [OGD, AIOY, AAA]
Design: [OGD]
Execution: [OGD]
Interpretation: [OGD]
Writing the paper: [OGD, AIOY]
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