FORECASTING PERFORMANCE IN IRAQI
STOCK EXCHANGE FOR THE OIL PRICE
THROW THE GM (1,2) MODEL AND THE
IMPACTS ON ECONOMIC GROWTH
Heshu Othm Faqe Mahmood
University of sulaimany College of administration & Economics Statistics and
informatics Dep.
heshu.faqe@univsul.edu.iq
Mohammed Aras Ali
University of sulaimany College of Commerce Economic Dep.
mohammed.aras@univsul.edu.iq
Zryan Jabar Raouf Ali
University of sulaimany College of Commerce Business Managment Dep.
zryan.raouf@univsul.edu.iq
Reception: 15/11/2022 Acceptance: 13/01/2023 Publication: 06/02/2023
Suggested citation:
F. M., Heshu Othm, A. A., Mohammed and R. A., Zryan Jabar (2023).
Forecasting Performance In Iraqi Stock Exchange For The Oil Price Throw
The GM (1,2) Model And The Impacts On Economic Growth. 3C Empresa.
Investigación y pensamiento crítico, 12(1), 311-322. https://doi.org/
10.17993/3cemp.2023.120151.311-322
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ABSTRACT
Iraq's oil industry is the country's main source of income. Iraq's manufacturing sector
has always been heavily dependent on the country's oil exports. Since the end of the
Iraq War, Iraq has expanded its output and is currently the region's second-largest
producer. For this investigation, the grey model was run using data on the monthly
international price of Iraqi oil from October 2020 through September 2022.
Researchers evaluated the MAPE and accuracy rate to choose which model to
employ for oil price forecasting, and we found that the GM(2,1) model was the best fit
for capturing the dynamics of the Iraqi oil market (precision rate = 96%, MAPE = 4%).
KEYWORDS
oil price, grey model, forecasting.
PAPER INDEX
ABSTRACT
KEYWORDS
INTRODUCTION
1. LITERATURE REVIEW
2. METHODOLOGY
2.1. THE GM (2,1) MODELS
2.2. THE GM (2,1) MODEL
2.3. EVALUATE PRECISION OF FORECASTING MODELS
2.3.1. RESIDUAL TEST
2.3.2. MEAN ABSOLUTE PERCENTAGE ERROR (MAPE)
2.3.3. PRECISION RATE(P)
3. APPLICATION
3.1. DATA DESCRIPTION
3.2. MODEL SPECIFICATION
3.3. FITTING GM(2,1) MODEL
3.4. GOODNESS OF FIT
4. CONCLUSIONS
REFERENCES
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INTRODUCTION
Petroleum, commonly known as crude oil, is a naturally occurring liquid that may be
converted into fuel and is found deep below the Earth's surface. Petroleum is a fossil
fuel formed from the gradual breakdown of organic matter; it is burned to generate
energy, heat buildings and machinery, and is also used in the production of plastics.
As a result of its widespread use, the petroleum industry has significant sway in
international affairs, and the wealth and business of countries such as Iraq, Saudi
Arabia, and the United Arab Emirates are heavily invested in the sector. The study
attempted to highlight the causal relationship between oil prices in the stock market
and economic growth in Iraq. The study is based on the hypothesis that there is a
bidirectional causal relationship between economic growth and global oil prices.
Therefore oil prices will have a significant impact on the structure of economic growth
in Iraq.
Iraq is one of the world's largest oil producers but is in an unstable political and
economic situation. According to OPEC data, Iraq is rated fifth in the world, behind
Venezuela, Saudi Arabia, Canada, and Iran. It should be noted that from 1986 until
2008, it was ranked second.
Oil was found inside Iraqi territory at the beginning of the twentieth century, and the
first oil well was dug by the reigning British authorities in Iraq in 1902, but the notion of
creating the global oil industry did not become popular until after World War II.
Since the sixties and seventies, Iraq's oil wealth has contributed to the country's
rapid economic expansion, which in turn has contributed to the country's development
and radical transformation. Iraq has some of the world's greatest oil reserves, with an
estimated (147) billion barrels of known reserves. This amounts to over 20% of the
world's total oil reserves. Oil is a lifeblood for Iraq, making it one of the world's most
dependent nations. In the past ten years, oil sales have paid for more than 99 percent
of exports, 85 percent of government spending, and 42 percent of GDP (GDP). This
over-reliance on oil makes the economy vulnerable to fluctuations, and budget
constraints limit room for manoeuvring in response to economic downturns. Iraq's
unemployment rate in January 2021 was over 10 percentage points greater than it
had been before COVID-19, at 22.7 percent, in a country of 40,2 million people. The
oil and COVID-19 shocks of 2020 jolted the economy, but it is beginning to show signs
of recovery. Following a significant decline of 11.3% in 2020, real GDP is predicted to
have increased by 1.3% in 2021. As oil output rises and COVID19 limitations are
relaxed, domestic economic activity is expected to return to pre-pandemic levels.
The oil sector worked to increase Iraqi revenues, which resulted in financial growth
in the budget, which prompted the Iraqi government to increase spending on training,
jobs, education, developing infrastructure, and increasing the salaries of government
employees.
The grey system theory, of which Professor Deng is the proponent, includes grey
prediction. A new model, GM(2,1), is presented to alter the linear structure of the
GM(1,1) model and broaden the range of applications for grey prediction theory.
Among the family of grey prediction models, it stands out as particularly significant.
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The GM(2,1) modeling approach is an offshoot of the GM(1,1) approach and satisfies
the same mechanisms. The GM(1,1) model uses an accumulating generation
operator (AGO) to reduce the noise in raw data and reveal hidden patterns.
1. LITERATURE REVIEW
Recent years have seen a proliferation of research aimed at advancing grey
prediction theory, and as a result, numerous optimized algorithms have arisen, vastly
increasing the range of grey prediction's potential applications. Here is a quick
synopsis of relevant works:
The grey prediction technique, which Song, F., and et al (2014) employed, is a
valuable tool for analyzing small datasets and making predictions for the near future.
Among the many significant grey models, the GM(2,1) model stands out. They
suggested a structure-optimized GM(2,1) model (SOGM(2,1)) to enhance accuracy
and predictability. There are three new insights within grey prediction theory that have
come out of this research. After constructing a new grey equation with an optimized
structure using the background sequence and the inverse accumulating generated
sequence, SOGM(2,1) model parameters are estimated using the method of least
errors. Second, using the obtained temporal response function, a reflection equation
is formed, and the process of solving it is derived. Finally, they proposed a different
approach to determining the initial values of the temporal response function. A
subsequent engineering evaluation uses the new model to anticipate highway
settlement. The results demonstrate the efficacy and practicality of SOGM(2,1)
compared to other models[1]. According to research by Junxu Liu et al (2020), load
forecasting is crucial for ensuring the power system's reliability and efficiently
allocating energy resources. In this study, we implement load forecasting of the power
system using the grey model theory. In this study, we apply the grey model theory to
implement medium- and long-term load forecasting. We also employ the posterior
difference technique to evaluate the model's performance in this context.
At last, a case study is presented to evaluate the technique's effectiveness [2]. In
addition, LiangZeng and ChongLiu (2023) created a novel approach to forecasting
China's per capita living electricity consumption using the grey modelling technique,
keeping in mind the aforementioned a variety of and mashup of shift patterns. As a
result, this work provided an improved version of the DGM(2,1) model by introducing
the polynomial component to investigate the growth patterns of different time-series
sequences. This was accomplished by fixing the modeling error in the traditional
DGM(2,1) model. This motivates the development of a brand-new model (denoted
DGM(2,1,kn)) for estimating the future electricity needs of China's population. To help
with the development of electrical power policies, forecasts of China's per capita living
electricity consumption in 2020 and 2025 have been developed[3]. A brief overview of
GM(1,1) models was provided by Evans, M. (2014), who also draws attention to a
trend-based alternative to traditional grey prediction theory. This method provides an
alternate strategy for estimating the parameters of the fundamental first-order
differential equation of the GM (1,1). Parameter estimates obtained using this
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alternative method are demonstrated to be more accurate, and the method's
straightforward graphical structure makes it simple to see. In this study, a more
universal generalization of the Grey-Verhulst model is proposed. When applied to the
intensity of steel use in the United Kingdom, yields very solid multi-step forward
predictions.
2. METHODOLOGY
2.1. THE GM (2,1) MODELS
The appropriate grey one-by-one model is for exponential pattern sequences; also,
it is used to show changes in monotonic patterns. While for other non-monotonic
wave, such as development sequences or satiate sequences that is sigmoid, we are
able to use GM two by one [5,6].
2.2. THE GM (2,1) MODEL
For raw data
, let i t a
generation accumulation and inverse accumulation generation be[5,7,8]
and ,
where and the adjacent sequence of
neighbour mean a generation of
Then
(2. 1)
Is show that GM(2,1) model ;
(2.2)
Theorem: For the sequences , as defined above, let
sequencesA(0) = (a(0)(1),a(0)(2), ……, x(0)(n))
A(1) = (a(1),a(1)(1),a(1)(2), ……, a(1)(n))
b(1) A(0) = (b(1)a(0)(2), ……, b(1)a(0)(n))
b(1)a(0)(k)=a0(k)−a(0)(k−1),k= 2,3, …, n
A(1)beY(1) =(y(1)(2),y(1)(3), ……, y(1)(n)).
d2a(1)
dt2
+α1
da(1)
dt
+b2a(1) =
c
A(0)A(1)Y(1)andb(1)a(0)
B
=
−a(0)(2)−y(1)(2)1
−a(0)(3)−y(1)(3)1
… … …
−a
(0)
(n)−y
(1)
(n)1
Y
=
b
(
1
)
a
(
0
)
(2)
b(1)a(0)(3)
…
b(1)a(0)
(
n
)
=
a(0)(2)−a(0)(1)
a(0)(3)−a(0)(2)
…
a(0)
(
n
)−
a(0)
(
n
−1)
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Also, in the least squares parametric sequence have estimated the
Of the G.M (2,1) is used as follows:
(2.3)
Theorem: For the solution of the G.M two by one winterization equation depend
the steps [9,10]:
1. If is a unique solution of and the
general solution of the corresponding homogeneous equation
, Then
represents a universal
method for solving the whitening equation for GM(2,1).
2.
The general solution to the preceding homogeneous equation requires
satisfying the following three conditions: (i) if the defining equation for a
has two distinct real roots
(2.4)
when the repeated root r is the characteristic equation,
;(2. 5)
when the two complex conjugate roots are the characteristic equation
(2.6)
3. In particular, one of the following three scenarios may represent a solution
to the winterization equation:
A. The characteristic equation root isn't zero, .
B. In the characteristic equation, zero is one of the2 distinct roots of, .
C. In the characteristic equation, zero is the only root of, .
2.3. EVALUATE PRECISION OF FORECASTING MODELS
To test the accuracy and the performance of the proposed model used, some
statistical tests and measurements, including residual test, MAPE, precision Rate and
Posterior Ratio(c) [6,8].
2.3.1. RESIDUAL TEST
Step1: calculate the relative error and absolute percentage error presented as
follows:
^
a
=[b1,b2,c]T
^
b=(C
T
C)−1C
T
Y
A(1)*
d2a(1)
dt2
+b1
da(1)
dt
+b2a(1) =
b
¯
A(1)
d2a(1)
dt2
+b1
da(1)
dt
+b2a(1) =
0
A(1) +¯
A(1)
r2+c1r+b2= 0
r1,r2,
¯
A(1) =c1er
1
t+c2er
2
t
¯
A(1) =ert(c1+c2t)
r1=b+iβandr2=b−iβ
¯
X(1) =eαt(c1cosβt+c2sinβt)
A(1)*=C
A(1)*=Ca
A(1)*=Ca2
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(2.14)
(2.15)
Step 2: calculate the two-step minimum and maximum of the relative error:
(2.16)
(2.17)
Step 3: find grey incidence coefficient
(2.18)
Of which the distinguishing coefficient p is 0.5
Step 4: find the degree of grey incidence
(2.19)
the GM model is qualified if
2.3.2. MEAN ABSOLUTE PERCENTAGE ERROR (MAPE)
To ensure that your forecasting model is as comprehensive as possible, you might
use the Mean Absolute Percentage Error metric. Here is how we characterize it
[7,9,10]:
(2.20)
Where : The actual value in period k
: Estimated worth for a k-period forecast.
And there are four levels of MAPE achievement:
∆
(0)(i)=a(0)(i)−^
a(0)(i)i= 1,2, 3,…,
n
∅
(i)=
∆(0)(i)
a
(0)
(i)
×100%i= 1,2, 3,…,
n
∆
min =min ∆
(0)
(i)
∆
ma x =ma x ∆
(0)
(i)
γ(
^
a(0)(k),a(0)(k)
)
=
∆
min
+p.∆
ma x
∆0i(
k
)+
p
.∆ma x
γ(
^
a(0),a(0)
)
=
1
n
n
∑
i=1
γ
(
^
a(0)(i),a(0)(i)
)
γ(^
a
(0)
,a(0)
)
> 0.6, whenp=
0.5
M
APE =1
n
n
∑
k=2
a(0)
(
k
)
−^
a
(0)
(k)
a(0)(k)×100
%
x(0)(k)
^
x(0)(k)
Precision rank
MAPE
Highly accurate
Good
Reasonable
Inaccurate
MAPE 0.1
≤
MAPE 0.01
≤
MAPE 0.15
≤
MAPE 0.05
≤
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The more depressed the MAPE, the higher the forecasting model's precision. In
general, the MAPE below 0.01 is an exact model and the MAPE between 0.01 - 0.05
is a good model with passable accuracy.
2.3.3. PRECISION RATE(P)
For further information on how close the stated prediction quantity is to the actual
value, see the section "Precision Rate" below, where p is the precision rate
[7,11,12,13].
1-MAPE (2.21)
The higher precision is the higher precision rate the forecasting model can achieve.
In general, a precision rate greater than 0.99 is an exact model, and a precision rate
between 0.99 -0.95 is a good model with fit accuracy.
3. APPLICATION
3.1. DATA DESCRIPTION
The data of this study has been taken from the world bank site, which
demonstrates the monthly oil price of Saudi Arabia in the international market from
Oct- 2020 to Sep- 2022.
Table 1. Represents the Monthly oil price of Saudi Arabia
3.2. MODEL SPECIFICATION
In the previous section, the collected data has been described to perform the grey
model GM (2,1).To make the appropriate model for forecasting the oil price.
p=
Precision rank
MAPE
Highly accurate
Good
Reasonable
Inaccurate
MAPE 0.95
≤
MAPE 0.90
≤
MAPE 0.90
≤
MAPE 0.99
≤
1234567891011 12
2018
69.05
65.78
70.27
75.17
77.59
79.44
74.25
77.42
82.72
75.47
58.71
53.8
2019 61.89 66.03 68.39 72.8 64.49 66.55 65.17 60.43 60.78 60.23 62.43 66
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3.3. FITTING GM(2,1) MODEL
By using the OLS method, the parameters of the GM(2,1) model has been
estimated depending on equation (2.3) with values of a and b ( and
), respectively.
Table 2. The actual predicted, and error values
0.001734
0.00012
^
a
=[a,b]T=
[0.001734
0.00012 ]
Ordinality
2
36.39
33.99
2.40
0.07
3
38.25
35.46
2.79
0.07
4
43.92
46.67
-2.75
0.06
5
49.47
51.99
-2.52
0.05
6
56.44
58.77
-2.33
0.04
7
60.43
65.27
-4.84
0.08
8
59.87
60.40
-0.53
0.01
9
62.8
58.78
4.02
0.06
10
68.58
74.31
-5.73
0.08
11
70.12
71.28
-1.16
0.02
12
65.68
64.18
1.50
0.02
13
69.09
67.01
2.08
0.03
14
78.51
76.09
2.42
0.03
15
76.45
79.83
-3.38
0.04
16
70.56
72.54
-1.98
0.03
17
80.33
78.04
2.29
0.03
18
89.41
91.95
-2.54
0.03
19
107.07
104.72
2.35
0.02
20
103.32
101.35
1.97
0.02
21
108.29
106.29
2.00
0.02
22
113.77
111.81
1.96
0.02
23
100.84
98.71
2.13
0.02
24
93.76
94.34
-0.58
0.01
Actual data
x(0)(k)
Model value
^
x(0)(k)
Error
ε(
k
)=
x
(0)(
k
)−^
x
(0)(
k
)
Relative error
∆
k=
ε(k)
x
(0)
(k)
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Figure 1. The scatter plot of the actual and predicted values of oil price
To test the performance of the proposed model, some statistical tests and
measurements, including MAPE and precision Rate. from the above table represent
model value and MAPE by GM(2,1) model, which is defined depending on eq (2.20).
Table 3. Represent the accuracy of the model
The data in the table above shows that the model has a high degree of accuracy,
as measured by the precision rate, p, which is proportional to the degree of
agreement between the forecasted amount and the actual value. p is specified as
0.96 in Eq. (2.21).
3.4. GOODNESS OF FIT
GM (2, 1) is a time series model then the goodness of fit of the model should be
tested by using the Augmented Dickey-Fuller test statistic; the results were as follow:
Table 4. Represent ADF test for the monthly oil price
Table 4 explains that the p-value of the ADF test equals (0.0034), and it is less than
(0.05). This result indicates that the model is significant.
Table 5. Demonstrates the forecasted values for three periods of time.
0
30
60
90
120
1
3
5
7
9
11
13
15
17
19
21
23
Actual data
Model value
Test GM (2,1)
MAPE 0.04
P 0.96
Test t-Sta=s=c Prob.*
Augmented Dickey-Fuller test sta=s=c -4.258028 0.0034
Period
Forecasted
Confidence Interval
Oct-22
95.76216
91.99667
99.52765
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4. CONCLUSIONS
From the results, we conclude that:
1.
The petroleum sector constitutes approximately (85%) of budget revenues,
(99%) of export revenues and (42%) of the gross domestic product (GDP) in
Iraq, and any changes in oil prices will affect all economic activities in Iraq.
2. (GM(2,1) model is more adequate for the series that it has a few data to forecast
in short terms).
3. From the results, it can be concluded that the GM(2,1) model is highly accurate
to represent the behavior of the Oil price rate in Iraq.
4.
The study shows that the MAPE for GM (2,1) model is equal to (0.04), which
does not need large data and displays high prediction accuracy.
5.
The model's great accuracy is indicated by the fact that the defined precision
rate p equals (0.96), where p is the rate at which the statement of the forecast
quantity matches the original value.
6. Depending on the Augmented Dickey-Fuller test statistic goodness of fit of the
model has been tested; the p-value of the test equals (0.0034), and it is less
than (0.05). This result indicates that the model is significant.
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