Using the Box-Jenkins ARIMA Approach for Long-term Forecasting
of 𝐂𝐎
𝟐
Emissions in Morocco
Mohammed Jamii, Naima Oumidou and Mohamed Maaroufi
Engineering for Smart and Sustainable System Research Centre, Mohamadia School of Engineers, Mohammed V
University in Rabat 11000, Morocco
Keywords: ARIMA, The Box-Jenkins, Forecasting.
Abstract: The Box-Jenkins ARIMA approach is one of the most essential methods to predict the variable carbon dioxide
CO
value with a proper model to describe the time variation of past data, and ensure security and
environmental protection (Wang, T, 2016). This study aimed to predict carbon dioxide emissions in Morocco
over the period 1928-2020, using the Box-Jenkins methodology, by building an econometric model for
forecasting carbon dioxide (CO
) emissions in Morocco during 1928-2020. Our study concluded that the time
series was stationary at the first difference. After examination, analysis, and comparison according to the Box-
Jenkins methodology through divers statistical tests, we have been proposed and building the best econometric
model to forecasting carbon dioxide (CO
) emissions in Morocco from the form ARIMA (2,1,1), Using the
proposed econometric model, our study concluded an estimate of the yearly forecast of carbon dioxide (CO
)
emissions in Morocco during the period between 2021-2040 which was Continuously increasing.
1 INTRODUCTION
Over the last few years, climate change is a
significant issue on the global political agenda due to
global warming (Nyoni et al. 2019). The CO
emitted
by human activities is primarily due to the
combustion of fossil fuels and deforestation (Daniel
A. Vallero, 2016). Based on international statistics,
the aviation and transport sector are most of the
reasons for the increase in GHGs over the last decade,
while other sectors have shown negative trends:
(Daniel A. Vallero, 2016). Prediction of future
behaviour of time series is one of the crucial topics of
statistical sciences, due to its necessity in all areas of
life, and its importance for the human element,
governments, and organizations in the planning and
implementation of the process of economic
development (Daniel A. Vallero, 2016).
Forecasting CO
emissions is an indispensable
part of a green energy economy (Pao et al, 2012). It is
essential to have a more in-depth view of the past
trajectory of Morocco's CO
emissions to reliably
forecast its future emissions (Pao et al, 2012).
This paper seeks to predict the evolution of carbon
dioxide emissions in Morocco during the next two
decades, 2021-2040 (Daniel A. Vallero, 2016). The
accuracy and validity of the ARIMA forecasting
method were tested by matching actual data with
forecast data (Nyoni et al, 2019).
The rest of the paper is structured as follows:
Section 2 presents a brief review of the literature
relevant to our research. Section 3 introduces the
methodology analysis. Section 4 sums up the data.
Empirical and predictive results are provided in
Section 5. Finally, the last section contains
concluding remarks.
2 LITERATURE REVIEW
In the literature, many articles use different
approaches such as time series econometrics, ANNs,
hybrids, etc. From various fields of engineering,
economics, science and, technology.
(Rahman and Hasan, 2017) used forty-four years
of time series data between 1972 and 2015 through
the use of ARIMA model, and they found that
ARIMA (0, 2, 1) model is the most appropriate model
to predict carbon dioxide in Bangladesh.
In other research on Bangladesh, (Hossain et al,
2017) forecasted the carbon dioxide emissions in
Bangladesh based on Box-Jenkins ARIMA from
496
Jamii, M., Oumidou, N. and Maaroufi, M.
Using the Box-Jenkins ARIMA Approach for Long-term Forecasting of CO2 Emissions in Morocco.
DOI: 10.5220/0010737600003101
In Proceedings of the 2nd International Conference on Big Data, Modelling and Machine Learning (BML 2021), pages 496-501
ISBN: 978-989-758-559-3
Copyright
c
2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
1972 to 2013, and they identified that ARIMA (12, 2,
12), ARIMA (8, 1, 3) are the most appropriate models
for predicting CO
emissions compared to the other
forecasting methods.
In China, (Nyoni. T, Chipo. M; 2019) forecasted
CO
emissions in the period 1960-2017, by using
Jenkins-Box (ARIMA) methodology, and the study
led to the selection of the most suitable model
ARIMA (1,2,1), to predict the total CO
emissions in
China in the coming ten years.
(Jamii and Maaroufi, 2021) predicted electrical
energy consumption using the ARIMA approach. The
most significant results indicate that the ARIMA
(1,1,1) model is the most appropriate model for
predicting electricity consumption in Morocco, and
among the results they found, an expected increase in
electricity consumption in Morocco by the end of
2030.
(Mitkov et al, 2019) predicted the energy
consumption of the Islamic Republic of Afghanistan
from 2001 to 2018, using the linear ARIMA model.
The results showed that energy demand would
continue to increase towards the end of 2024.
(Sangeetha and Amudha, 2018) predicted CO
emissions in India, and their results illustrated that the
PSO method could achieve a very efficient and
accurate estimation compared to the MLR model.
In Morocco, (Nafil et al, 2020) investigate three
forecasting methods, namely; ARIMA, Temporal
causality modelling, and Exponential smoothing, to
calculate the energy demand forecasts of Morocco in
2020.
This study will apply the ARIMA approach to
model and forecast CO
emissions in Morocco.
3 METHODOLOGY
3.1 ARIMA Model
The ARIMA model is a univariate model that tends
to identify a single variable as an autoregressive
integrated moving average process (Awe et al, 2020).
It includes a composition of three kinds of random
processes, the performance of which is expressed as
ARIMA (p, d, q), where p is the order of the
autoregressive process AR (p), d is the degree of
integration of the process I (d), and q is the order of
the moving average MA (q) (Cheikh Sarr et al, 2021).
The ARIMA (p, d, q) model is generally organized as
follows:
𝑌
𝑡1
𝑌
𝑡
𝐶ℇ
𝑡
(1)
Where, t is a white noise perturbation term. Then, 𝑌
𝑡
is then considered to be generated by an integrated
first-order process, and it is notated as I (1).
Compactly, the model can be written as:
∇𝑌
𝐶ℇ
(2)
Where,
∇ 1𝐵
(3)
Likewise, an integrated process of order d is indicated
by I(d) and can be expressed as follows:
∇
𝑑
𝐶ℇ
𝑡
(4)
The ARIMA process of order p, d, and q is given as
ARIMA (p, d, q), and can be represented compactly
as follows:
𝜑B ∇
𝑌
𝐶 𝜃
𝐵
ℇ
(5)
4 DATA COLLECTION
This study is based on 92 years of observations (i.e.,
1928 - 2020) of CO2 annual emissions (Mt) in
Morocco. All the data used in this study were
extracted from the World Bank's online database.
Figure 1: The annual CO
emissions in Morocco for the
period 1928-2020.
We note that our series is not stationary, as shown by
an upward trend over the period 1928- 2020. This
indicates that the mean and variance of annual CO
emissions change over time. In addition, carbon
dioxide emissions in 2020 dropped by 7% in 2020,
the most significant decrease on record, as countries
worldwide, imposed lockdowns and restrictions on
Using the Box-Jenkins ARIMA Approach for Long-term Forecasting of CO2 Emissions in Morocco
497
movement to curb the spread of the coronavirus
pandemic (IEA, 2021).
4.1 The ADF Test for Stationarity
After applying Augmented Dickey–Fuller test on our
series, we found that the ADF value is 3.713814,
which is superior to the critical value of significance
level of 10%, 5% and 1%, respectively. Hence, it
cannot reject the presence of the unit root.
Based on
the unit root test, the CO
emission series in Morocco
seems to contain a unit root. Indeed, our series is non-
stationery. Indeed, the ADF value at the first
difference is -8.915777, which is below the critical
value of the significance level of 10%, 5% and 1%,
respectively. It is stationary at the 1st difference
(Jamii and Maaroufi, 2021). The specific results are
provided in Table 1.
Table1: Augmented Dickey–Fuller test
Test
critical
values
(%)
Unit Root Test
(Level)
Unit Root Test
(First diff)
T Statistic
3.713814
Prob
1.00
T Statistic
-8.91577
Prob
0.00
1 -3.513 -3.532
5 -2.897 -2.906
10 -2.586 -2.590
Figure 2: The time series plot of the first difference of CO
emissions of Morocco
The next step is to simulate the procedure for the
CO
emissions
series. We start by using the correlogram of
the stationary series, and we can obtain from (Fig 3
and Fig 4) the results of the correlation analysis. From
the autocorrelation coefficients and partial
autocorrelation coefficients, we attempt to adjust a
random time series.
Figure 3: The first-order autocorrelation coefficients of
carbon dioxide emissions
Figure 4: The first-order partial autocorrelation coefficients
of carbon dioxide emissions
4.2 Evaluation of ARIMA Models
Table 2: overview of information criteria
Model
AIC
BIC
HQIC
Log
Likelihoo
d
ARIMA
(1,1,1)
318.430
325.995
321.483
–156.215
ARIMA
(1,1,2)
306.486 316.933 310.917 –149.423
ARIMA
(2,1,1)
305.739* 315.739* 309.727* –148.826*
ARIMA
(2,1,2)
307.198 319.807 312.287 –148.599
ARIMA
(3,1,1)
307.130 319.739 312.219 –148.565
In order to obtain the best ARIMA, we applied
selection criteria such as log-likelihood, AIC (Akaike
information criterion), BIC (Bayesian information
criterion) and HQC (Hannan Quinn information
criterion). The ARIMA (2, 1, 1) model is chosen as
the optimal model due to the lowest value of AIC,
BML 2021 - INTERNATIONAL CONFERENCE ON BIG DATA, MODELLING AND MACHINE LEARNING (BML’21)
498
BIC and HQC and the maximum value of Log-
Likelihood as shown in Table 2.
Figure 5: Residuals diagnostic plots of ARIMA (2,1,1)
5 RESULTS & DISCUSSION
5.1 Descriptive Statistics
We notice from the table below that Jarque-Bera (JB
= 454) indicates a critical probability of 0.52. We
accept H0 of normality of residuals. Therefore,
Homoscedasticity residues are verified. Residues are
white noise processes.
Table 3: Descriptive Statistic from ARIMA Model
Mean Std Skew Kurtosis JB Prob
19.15 21.09 0.58 8.70 454 0.52
5.2 Estimation of ARIMA (2,1,1)
The parameters of ARIMA (2,1,1) are listed in table
3. Thus, the forecasted model can be written as
follows:
𝑌
0.4956𝑌
0.4937𝑌
0.8475ℇ
–
ℇ
(6)
Table 4: ARIMA (2, 1, 1) Final parameter estimates
Variable Coef Std err Z Pb
AR (1) 0.4956 0.075 6.583 0.000
AR (2) 0.4937 0.076 6.483 0.000
MA (1) -0.8475 0.085 -10.006 0.000
A comparison between the actual data obtained from
the dataset and the predicted data based on the
ARIMA model is presented in Fig. 6. It can be seen
that the two graphs match well. The predicted data
follow the shape of the data graph. This shows the
extent of convergence of the model estimated from the
real data.
Figure 6: Actual, fitted plot of CO
emission from model
selected ARIMA (2,1,1)
5.3 Forecast Graph
Based on the estimated model, 𝐶𝑂
emissions are
provided over the next two decades. The results in
Figure 7 show that by 2040, annual CO2 emissions
will continue to increase from 69.18 million tonnes of
carbon dioxide equivalent to 109.25 million tonnes of
carbon dioxide equivalent. However, this increase is
due to the growth of the Moroccan population in
recent years, and consequently, the need for
electricity is increasing. Indeed, the main sources of
carbon dioxide emissions in Morocco are electricity
generation and transport sector. According to the
latest statistics, in 2016, the electricity sector
generated 39% and the transport sector 31% of total
emissions. The rest came from industry (13%),
residential and commercial buildings (12%) and
agriculture (5%). (International Energy Agency,
2019).
Figure 7: Forecast of CO
emissions over the next two
decades (2021 to 2040)
Using the Box-Jenkins ARIMA Approach for Long-term Forecasting of CO2 Emissions in Morocco
499
5.4 Policy Implications
In this paper, we have discussed the forecasting of
CO
emissions in Morocco based on the Jenkins
approach (ARIMA). The results show that the
ARIMA method performs well in predicting CO
emissions for the next 20 years and offers increased
CO
emissions. These results are essential for the
Moroccan government. This knowledge can be used
in the decision-making process, such as energy
control in the transport sector. Some
recommendations can be listed as follows:
- Support the integration of renewable energy sources
in homes for householder self-consumption.
-The adoption of electric cars is also highly
recommended, as it will decrease the transport
sector's emissions, especially if the energy needed to
run them is produced by renewable sources.
-Allowing discounts on the purchase of low
consumption and environmentally friendly household
appliances.
-Initiate policy actions such as increasing taxes on the
polluting companies, particularly those that burn
fossil fuels in their daily production activities.
6 CONCLUSIONS
In this study, we developed an ARIMA model to
forecast CO
emissions in Morocco using the Box-
Jenkins time series approach. The historical CO
emissions data have been used to develop several
models, and the appropriate model selected based on
four performance criteria: AIC, BIC, HQIC, and
maximum likelihood. As a result, we found that the
ARIMA (2,1,1) model is the model that minimizes
the four previous criteria. The results obtained prove
that this model can be used to model and forecast
future CO
emissions over the next two decades in
Morocco.
The results of this study are vital as they can be
used by researchers, stakeholders and, the Moroccan
government to take adequate measures to implement
a sustainable climate policy. In addition, an accurate
forecast of CO
emissions on our territory will help
the country's political leaders to negotiate a climate
fund with the international community.
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