Asian Research Journal of Mathematics
17(3): 35-54, 2021; Article no.ARJOM.68132
ISSN: 2456-477X
__________________________________________________________________________________________________________________________________
Comparative Modelling of Price Volatility in Nigerian Crude
Oil Markets Using Symmetric and Asymmetric GARCH
Models
Deebom Zorle Dum1*, Mazi Yellow Dimkpa2, Chims Benjamin Ele2,
Richard Igbudu Chinedu2 and George Laurretta Emugha3
1
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
Statistics Department, Ken Saro-Wiwa Polytechnic, Bori, Rivers State, Nigeria.
2
Department of Mathematics, Ignatius Ajuru University of Education, Port Harcourt, Nigeria.
2
Authors’ contributions
This work was carried out in collaboration among all authors. Author DZD designed the study, performed
the statistical analysis, wrote the protocol, and wrote the first draft of the manuscript. Authors MYD and
CBE managed the analyses of the study. Authors RIC and GLE managed the literature searches.
All authors read and approved the final manuscript.
Article Information
DOI: 10.9734/ARJOM/2021/v17i330282
Editor(s):
(1) Prof. Megan M. Khoshyaran, Economics Traffic Clinic - ETC, France.
(2) Danilo Costarelli, University of Perugia, Italy.
(3) Dr. Nikolaos D. Bagis, Aristotle University of Thessaloniki, Greece.
Reviewers:
(1) Siwapong Dheera-aumpon, Kasetsart University, Thailand.
(2) Pavel Levin, St. John’s University, USA.
Complete Peer review History: http://www.sdiarticle4.com/review-history/68132
Original Research Article
Received 01 March 2021
Accepted 05 May 2021
Published 18 May 2021
_______________________________________________________________________________
Abstract
The study aimed at developing an appropriate GARCH model for modelling in Nigerian Crude Oil Prices
Markets using symmetric and Asymmetric GARCH models while the specific objectives of the study include
to: build an appropriate Symmetric and asymmetric Generalized Autoregressive Conditional Heteroskedacity
(GARCH) model for Nigerian Crude Oil Prices, compare the advantage of using Symmetric and Asymmetric
GARCH. The data for the study was extracted from the Central Bank of Nigeria online statistical database
starting from January, 1982 to December, 2018. The software used in estimating the parameters of the model
is Econometric view (Eview) software version ten (10). Two classes of models were used in the study; they
are symmetric and Asymmetric GARCH models. The results of the estimated models revealed that
________________________________________
*Corresponding author: Email: dumjolly@gmail.com, dumzorle@yahoo.com;
Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
Asymmetric GARCH model (EGARCH (1,1) in student’s-t error assumption gave a better fit than the first
order Symmetric GARCH models. Also, Using EGARCH (1,1) models with their corresponding error
distribution in estimating crude oil price was found that the larger the size of the estimated news components
of the model, the higher the negative news associated with high impact of volatility. This means that
conditional volatility estimated using EGARCH model has strong asymmetric characteristic which is prone to
news sensitivity. Based on the above findings, recommendations were made in the study.
Keywords: Modelling; crude oil; markets; symmetric; asymmetric.
1 INTRODUCTION
1.1 Background to the study
When there is an unstable economic situation, crude oil price is usually associated with negative return and
high variance. According to Dritsaki [1], the larger the risk in stock price changes in monetary policies
during these unstable periods would reduce market efficiency, and is most likely to affect the consistency in
macroeconomic relationships. Risks associated with instability in the returns on prices and sales of crude oil
is one of the major challenges facing both oil producing countries and major buyers of crude oil in the world
today. This risk took the form of response to good and bad news due to disaster, insurgency, political
disorder, political agitations etc. Sequel to the occurrence of these unforeseen circumstances, crude oil
market prices experienced fluctuation and becomes highly volatile. The degree of price fluctuation or
volatility in crude oil markets has increasingly attracted attention in recent period. In time series,
econometrics as well as other financial literature; and according to Dritsaki [1], it has been recognized as one
of the most significant economic phenomena. Researchers like Zheng, et al. [2] have argued that price of
crude oil is volatile, so it reduced welfare and competition by increasing consumer costs. Meanwhile,
Apergis and Rezitis [3], observed that price volatility of this product makes both producers and consumers of
this product to be uncertain, which most times, oligarchy see it an opportunity to take advantage of this
situation to advance their selfish interest.
Although, commodity prices in general are volatile, and in particular crude oil prices and its constituents like
Kerosene, Petrol, etc. are renowned for their continuous volatile nature. Returns on prices and sales of crude
oil have undergone dramatic changes over the past years, the desire to formulate policy measure or
intervention to prevent it from going into volatility have not been achieved due to irregularities in the market
system. Findings in this area show that returns on prices and sales of crude oil in the markets still remain
high. Besides, crude oil price volatility in monetary assets is still an area in which little empirical attention
has been paid in Nigeria. Therefore, it appears worthwhile to devote effort in modelling price volatility in
Nigerian crude oil markets using symmetric and Asymmetric GARCH models with a view to prefer
solutions to the problems confronting crude oil markets
2 METHODOLOGY
2.1 Sources of data and software used in the study
Data used for this study was sourced for and extracted from the official website of the Central Bank of
Nigeria [4]. The data comprise of monthly crude oil export prices, sales in Naira/Dollar per barrel. It was
extracted between the month of January, 1988 and March, 2019. These make a total of 396 data points. The
software used in estimating the parameter of the model was Econometric view (Eview) software version ten
(10).
2.2 Data transformation
According to Tsay [5], time series data are divided into two categories; the first category is the stationeries
and the second category is then on-stationary. He further explained that the Stationarity of a data set can be
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
tested with augment Dickey-Fuller (ADF) test whereas the Non-stationary time series data can are usually
transformed into stationary data by using log return transformation. Therefore, this is done by assuming
CPRt
to denote the data crude oil Price Return at time t and
return transformation can be written as:
CRn denotes the log return of the data, the log
CPRt 100
CRn log
CPRt 1 1
(2.1)
Where t = 1, 2, 3 …. t-I and CRn represents the return on crude oil pieces, CPRt is crude oil export price at
time t in Naira per Dollar, CPRt-1 represents crude oil price at lag t (t-1) or precious time at t minus one, log
represents logarithms, and 100 is a constant value (Number) the data used in this study was differenced (D)
in order to get rid of outlier as well as to attain stationarity of the data.
2.3 Model specification
Black [6] defined model specification as a simplified system used to simulate some aspects of the real or
actual economy. It is a form or specified views of reality design to enable the researcher describe the
essence or inter-relationship within the variables or condition under the study. However, in line with the
objectives of this study, two classes of models used in the study are symmetric and asymmetric GARCH
models.
2.3.1 The standard symmetric GARCH models
The process of developing standard symmetric GARCH commence with the autoregressive moving average
(ARMA) model with (p.q) order of the log return data r1 can be written as
p
q
i 1
j 1
rt 0 i rt 1 j t j t
Where
0
2.2
denotes the constant, denotes the order of autoregressive (AR) Model, 1, 2,..., denotes the AR
parameters, q denotes the order of the moving average (MA), 1,2,3,…,q denotes the MA parameter, and t
denotes the model residual at time (t). Tsay [6] further observed that the highest MA order determined by
ACF plot which cut off after the pth lag while AR order determined by PACF plot which cut off after the qth
lag. The Heteroskedasticity effect of ARMA model can be tested with Lagrange multiplier (LM) test.
Therefore, by definition the standard GARCH model used in the estimation of Crude Oil price returns , we
considered the residual of the ARMA process obtained in model in equation (3.2) and the residual could
written
(2.3)
as
shown
below
t tt
for
t ~ N (0,1)
and
t / f t 1 ~ N (0, t2 )
The standard symmetric GARCH (1, 1) model can written as thus
t2 0 1 t21 t21
(2.4)
Whereα0 ≥ 0, α1 ≥ 0 and β ≥ 0, i.e. all these parameters must be positive in order to guarantee a positive
conditional variance, and where 1 + <1 represents the persistence of shocks to volatility [7]. Following
Klaassen [8] and Haas et al. [9] the study adopted Student’s-t and normal distribution for ɛt. Also, another
example of the standard GARCH model is the Generalized Autoregressive Conditional Heteroskedasticity in
means (GARCH-M). According to Brooks [10], this model suggests that the mean return of a financial data
series would be related to the conditional variance or standard deviation of the economic data series itself
and that this model estimate mostly high risk associated with financial time series data. The GARCH Model
is written as :
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
Mean equation
Rcop = t2 t
Variance Equation:
(2.5)
Rcop t
T
t
2
t
(2.6)
Similarly, 0, 0 and 0 for Rcop , t are all parameters are to be estimated is called the
risk premium parameter, and it is mostly not interpretable in practice. According to Brook (2006), this model
captured different form influence of volatility on the conditional variance
2
2.3.2 Standard asymmetric GARCH models
In another development, the study considered asymmetric GARCH model and some of the examples of the
asymmetric GARCH model are used TGARCH, EGARCH, PARCH and CGARCH.
The threshold Generalized Autoregressive Conditional Heteroskedasticity TGARCH (1,1) model
According to Brook [10], the TGARCH was found by Glisten et al. in 1993 the variance of the model was
define as:
t2 0 1 t2 1 I 1t 0 t2 I
0 , 1 ,
and
1 0 ,
t 1
1
(2.7)
t 1
where I t 1 is an indicator function, and if t 1
0, I
t 1
=i,j
Otherwise ,
I t 1 0 0
In equation (3.4), when t 1 0 this simply multiplies good news whereas t 1 0 implies bad news and
under these condition, (shocks) of equal magnitude have differential effects on conditional variances [11].
Similarly, good news has an impact magnitude of 1 while bad news has an impact magnitude of 1 + I
which in away cause increase in volatility. Also, if I1 >0, this invariably means that there is the existence of
leverage effect of the 1st order. When I1=0, then this means that news impact is asymmetric in nature.
Although, given the standard GARCH model in equation (3.6) assumes that the effect of positive and
negative information is symmetric which may not be completely applicable in a market situation [7]. Nelson
[12] proposes the Exponential GARCH (EGARCH) model to examine the asymmetric features of asset price
volatility, and which according to him the logarithm of the conditional variances of Crude Oil price returns
can be stated as thus:
2
log
=
2
t
0 01 1 0
0
>0 and
2
1
a t 1
2
t 1
1 0 .
+
e
t 1
t 1
Similarly,
news respectively whereas the total effects
1 t 1 respectively.
+
log t
2
-1
(2.8)
t 1 0 simply depict good news and t 1 0 means bad
of bad and good news are given as 1 t 1 and
In this case, we accept the null hypothesis that = 0 which shows that there is the presence of leverage
effect and this simply mean bad news have stronger effect than good news on the volatility of the return
series [11].
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
2.3.2.1 The power ARCH (PARCH) model
p
q
i 1
j 1
t i ( t i i t i ) j t j
Where
(2.9)
0, i 1 for i=1,……., , i =0 for i> , and p
(2.10)
The components GARCH (CGARCH) model
It allows mean reversion to a varying level mt
t21 is
t2 mt ( t21 ) ( t21 )
(2.11)
mt o ( mt 1 ) ( t21 t21 )
(2.12)
still the volatility, while
mt takes
the place of
which could also be time varying long-run
t2 mt which converges to zero
powers of ( ) . The model (3.12) describes the long run component mt , which converges to
powers of .The models stated in equation (3.3) to (3.11) define the standard GARCH model.
volatility. The model (3.11) describes the transitory component,
with
with
2.3.3 Error distributional assumptions
In modelling the conditional variance of crude oil price, five conditional distributions for the standardized
residuals of the price returns modernism were considered and they include; the Gaussian (Normal), student’s
–t, Generalized, student’s –t with fixed parameter(v=3) and Generalized with fixed parameter(v=3) .
2.3.3.1The gaussian (normal) distribution
The Gaussian (Normal) error distribution assumed a log-likelihood contribution is of the form;
T
1 T y y
1 T
1
LogL ( t ) L ( t ) Log [2 ] log( t2 ) t 2 t
2 t 1
2 t 1
2
t
t 1
2
(2.24)
2.3.3.2 The student’s –t error distribution
The student’s –t error distribution assumed a log-likelihood contribution is of the form;
2
v
v
[
2
]
2
'
2 1
1
Log 2 v 1 Log 1 y t X t
LogL ( t ) log
t
2
2
2
2
2
t v 2
v 1
2
Where
t2
is the variance at time t and the degree of freedom
(2.25)
v >2 controls the tail behaviour.
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
2.3.3.4 The generalized, distribution
The Generalized (GED) likelihood function is specified as:
3
3
1
'
r yt X t
1
1
r
2
r
Log Log
LogL( t ) log
t
3 r 2 2
2
2 1
t r
r 2
r
2
2
(2.26)
r >0 is the shape of the parameter which basically account for the skewed properties of the returns of the
series under estimation. The higher the value of r , the heavier the weight of the tail. Omorogbe and
Ucheoma [13] revealed that the Generalized (GED) turns to be a Gaussian (Normal) error distribution if r
=0 and flat-tailed if r<2.
2.3.3.5 The student’s –t with fixed parameter (v=3) error distribution
The student’s –t error distribution assumed a log-likelihood contribution is of the form;
When v=3, we substitute the value into the model in equation
LogL
Where
t2
3
1
2
log
( t )
2 2
2
2
1 Log
2
(2.25)
y
2 Log 1
2
t
is the variance at time t and the degree of freedom
t
X t'
2
2
t
(2.27)
v =3 controls the tail behaviour.
2.3.3.6 The generalized with fixed parameter(r =3) error distribution
The Generalized (GED) likelihood function is specified as thus: When v=3 , we substitute the value into the
model in equation (3.24), we have
3
1
1
r
LogL ( t ) log
3 r 2
2
r 2
1 Log
2
2
t
3
y t X t'
r
r
Log
1
2
t r
3
3
1
'
3 yt X t
1
1
3
Log 2 Log 3
LogL ( t ) log
t
3 3 2 2
2
2 1
t 3
3 2
LogL
(
t
1
1
1
9
Log
)
log
2
2
9
4
2
t
Log
3 y
t
2
t
X
'
t
1
3
2
3
2
2
r
2
(2.28)
3
2
2
(2.29)
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
r =3 is the shape of the parameter which basically account for the skewed properties of the returns of the
series under estimation. The higher the value of r , the heavier the weight of the tail.
3 RESULTS
First, we present the raw data. Fig. 1 is a plot of the raw data with time (years) on the horizontal axis and
Crude Oil Price (Dollar/Barrel) on the vertical axis. This portrays the direction and moving trend of the
variable under study. This is followed by Table 1 which contains the results of descriptive statistics of the
returns on crude oil price (Dollar/Barrel). This is carried out in order to know whether the returns on crude
oil price data obey the normality assumption
140
Crude Oil Price (COP)
120
100
80
60
40
20
0
1985
1990
1995
2000
2005
2010
2015
Years(Month)
Fig. 1. Time plot on crude oil price (dollar/barrel)
Table 1. Descriptive statistic of the returns on prices and sales of crude oil
Mean
Median
Max
Min
0.123
0.484
47.084
-32.105
Std.
Dev.
8.909
Skewness
Kurtosis
-0.092
5.535
JarqueBera
119.210
P-value
0.000
The result of the estimated ARMA Model which was done in order to obtain the residual from the ordinary
linear square regression equation
DCop = 0.119 + 0.230* t2 1
(0.772) (0.0000)
(3.1)
The model in equation 4.1 was estimated in order to obtain the residual from the Autoregressive Moving
Average which was used to test for the presence of volatility clustering.
To portray the volatility clustering of Crude Oil Prices (Dollar/Barrel), a graphical representation is shown in
Fig. 2. This is done in order to be sure that the variable on Crude Oil Prices (Dollar/Barrel) exhibits volatility
clustering and also be good enough for GARCH Estimation.
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
Returns on Crude Oil Price(COP)
50
40
30
20
10
0
-10
-20
-30
-40
1985
1990
1995
2000
2005
2010
2015
Years(Month)
Fig. 2. Volatility clustering on crude oil prices (dollar and barrel)
An estimation of heteroskedasticity is presented in Table 2. This represents the results of the
heteroskedasticity (ARCH Effect) estimation. This is done using the residual (standard error) obtained from
the ARMA process and this helps in verifying that variance of the residual is constants. If it is not constant,
then if it is heteroskedastic, the GARCH model will be appropriate in capturing the effect of volatility in the
returns of the series.
3.1 Heteroskedasticity (ARCH effect) estimation
Table 3 shows the results obtained from the estimation of classes of symmetric GARCH model with their
corresponding error distributional assumptions.The symmetric GARCH models comprises of GARCH(1, 1)
and GARCH(1, 1) in Mean with their corresponding normal, students, Generalized, Student’s t- with fixed
degree of freedom (V=3), and GED with fixed degree of freedom(V=3).
The results obtained from the estimation of classes of asymmetric GARCH model with their corresponding
error distributional assumptions is shown in Table 4.
Table 5 Shows the results obtained from the estimation of classes of asymmetric GARCH model with their
corresponding error distributional assumptions.
The best fitted model from the thirty estimated models based on the Schwarz information criterion (SIC) can
be written as thus:
The mean Equation:
COPt = -0.146 + 0 .199 t21
(0.614) (0.000)
(3.2)
Table 2. Testing for the presence of an ARCH effect
F-statistic
Obs*R-squared
4.891
23.463
Prob. F(5,431)
Prob. Chi-Square(5)
0.0002
0.0003
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
Table 3. Estimation of standard GARCH model (error distributional assumption)
Model(s)
GARCH(1,1)
Estimator(s)
Parameter(s)
Normal
Student’s-t
GED
Mean ()
Intercept()
-0.144
(0.541)
0.167
(0.00)
1.972
(0.069)
0.437
(0.000)
0.635
(0.000)
0.802
6.976
7.023
6.995
0.153
(0.145)
-0.942
(0.129)
0.163
(0.001)
1.824
(0.096)
0.437
(0.000)
0.639
(0.000)
0.802
6.973
7.029
6.995
-0.003
(0.989)
0.179
(0.00)
1.707
(0.105)
0.364
(0.000)
0.687
(0.000)
0.866
6.962*
7.017*
6.983*
0.170
(0.09)
-0.914
(0.137)
0.172
(0.000)
1.574
(0.140)
0.367
(0.000)
0.688
(0.000)
0.860
6.958*
7.023*
6.983*
-0.058
(0.823)
0.177
(0.000)
1.865
(0.103)
0.397
(0.000)
0.661
(0.000)
0.838
6.970
7.025
6.992
0. 157
(0.126)
-0.889
(0.145)
0.172
(0.001)
1.656
(0.142)
0.399
(0.000)
0.666
(0.000)
0.838
6.967
7.032
6.992
ARCH()
Variance()
Intercept()
ARCH()
GARCH()
Volatility Impact()
Model Selection Criteria
GARCH-M
Mean ()
( + )
AIC
SIC
HQC
@SDRT (GARCH)()
Intercept
ARCH
Variance()
Intercept
ARCH()
GARCH()
Model Selection CRITERIA
(+)
AIC
SIC
HQC
Student’s t- with Fix
DF (V=3)
0.096
(0.706)
0.198
(0.000)
1.967
(0.247)
0.518
(0.000)
0.741
(0.000)
0.939
7.001
7.047
7.019
0.131
(0.063)
-0.828
(0.148)
0.186
(0.000)
1.925
(0.253)
0.533
(0.001)
0.736
(0.000)
0.922
6.996
7.052
7.018
GED with Fix Df
(V=3)
-0.379
(0.030)
0.143
(0.000)
2.013
(0.056)
2.031
(0.000)
0.577
0.000
0.720
7.063
7.109
7.081
0.106
(0.255)
-0.946
(0.096)
0.146
(0.000)
2.180
(0.051)
0.594
(0.000)
0.580
(0.000)
0.726
7.063
7.119
7.085
Min. AIC
(6.962)
(6.958)
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Table 4. Estimation of asymmetric GARCH model (Error distributional assumption)
Model(s)
Equation(s)
Parameter(s)
Normal
Student’s-t
Mean ()
Intercept()
-0.193
(0.495)
0.191
(0.000)
-0.077
(0.586)
0.632
(0.000)
-0.068
(0.145)
0.898
(0.000)
1.089
6.953
7.008
6.974
-0.263
(0.345)
0.175
(0.000)
1.888
(0.067)
0.348
(0.000)
0.124
(0.235)
0.656
(0.000)
1.004
6.978
7.034
7.000
-0.146
(0.614)
0.199
(0.000)
-0.089
(0.502)
0.537
(0.000)
-0.096
(0.111)
0.919
(0.000)
1.118
6.942*
7.007*
6.968*
-0.134
(0.641)
0.196
(0.000)
1.569
(0.102)
0.243
(0.001)
0.162
(0.163)
0.719
(0.000)
0.962
6.962*
7.027*
6.987*
ARCH()
Variance()
Intercept()
ARCH()
EGARCH (1,1)
Asymmetric()
GARCH()
Volatility Impact()
Model Selection Criteria
Mean ()
(+)
AIC
SIC
HQC
Intercept()
ARCH()
Variance()
Intercept()
ARCH()
TGARCH (1,1)
Asymmetric()
GARCH()
Volatility Impact()
Model Selection Criteria
(( + ))
AIC
SIC
HQC
GED
-0.151
(0.597)
0.195
(0.000)
-0.083
(0.567)
0.589
(0.000)
-0.076
(0.171)
0.908
(0.000)
1.103
6.950
7.015
6.976
-0.175
(0.537)
0.188
(0.000)
1.741
(0.099)
0.299
(0.000)
0.133
(0.251)
0.688
(0.000)
0.987
6.972
7.036
6.997
Student’s- with
Fix DF (V=3)
-0.038
(0.889)
0.214
(0.000)
-0.106
(0.467)
0.608
(0.000)
-0.125
(0.205)
0.946
(0.000)
1.160
6.989
7.045
7.011
-0.015
(0.954)
0.219
(0.000)
1.628
(0.275)
0.308
(0.090)
0.287
(0.216)
0.773
(0.000)
1.081
7.001
7.056
7.023
GED with Fix Df
(V=3)
-0.329
(0.198)
0.197
(0.000)
-0.058
(0.678)
0.8227
(0.441)
-0.029
0.441
0.867
(0.000)
1.016
7.028
7.084
7.050
-0.484
(0.043)
0.147
(0.000)
2.018
(0.057)
0.537
(0.000)
0.104
(0.313)
0.587
(0.000)
1.124
7.066
7.121
7.088
Min. AIC
(6.942)*
(6.962) *
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Table 5. Estimation of asymmetric GARCH model (error distributional assumption) continuation
Model(s)
Equation(s)
Parameter(s)
Normal
Student’s-t
GED
Mean ()
Intercept()
( + )
AIC
SIC
HQC
Intercept()
-0.177
(0.487)
0.166
(0.000)
0.353
(0.077)
0.281
(0.001)
0.697
(0.000)
0.674
(0.000)
0.955
6.969
7.034
6.995
-0.068(0.809)
ARCH()
0.181(0.000)
Intercept()
5567.
(0.889)
1.000
(0.000)
0.035
(0.781)
0.582
(0.000)
1.582
6.970*
7.035*
6.995
-0.144
(0.628)
0.192
(0.000)
0.402
(0.178)
0.275
(0.000)
0.729
(0.000)
0.882
(0.018)
1.107
6.957*
7.031*
6.986*
0.071
(0.801)
0.191
(0.000)
406.471
(0.845)
0.993
(0.000)
-0.143
(0.003)
0.573
(0.227)
1.566
6.974
7.057
7.000*
-0.125
(0.662)
0.186
(0.000)
0.403
(0.152)
0.286
(0.000)
0.709
(0.000)
0.810
(0.019)
1.019
6.965
7.039
6.994
-0.006
(0.983)
0.185
(0.000)
8811.27
(0.759)
1.000
(0.000)
0.361
(0.010)
0.616
(0.000)
1.616
6.967
7.041
6.996
ARCH()
Variance()
Intercept()
ARCH()
PARCH (1,1)
Asymmetric()
GARCH()
Volatility Impact()
Model Selection Criteria
CGARCH (1,1)
Mean ()
Variance()
ARCH()
Asymmetric()
GARCH()
Volatility Impact()
Model Selection Criteria
( + )
AIC
SIC
HIQ
Student’s- with Fix
DF (V=3)
-0.049
(0.859)
0.212
(0.000)
0.450
(0.410)
0.335
(0.007)
0.777
(0.000)
1.058
(0.056)
1.393
7.005
7.065
7.026
0.309
(0.304)
0.187
(0.000)
52576
(0.459)
1.000
(0.000)
0.075
(0.327)
-0.800
(0.000)
0.200
7.035
7.100
7.061
GED with Fix Df
(V=3)
-0.100
(0.000)
0.148
(0.000)
0.247
(0.007)
0.261
(0.001)
0.665
(0.000)
0.337
(0.018)
0.597
7.057
7.121
7.082
-0266
(0.322)
0.187
(0.000)
5121.91
(0.000)
1.000
(0.000)
0.511
(0.004)
0.454
(0.027)
1.454
7.045
7.110
7.070
Min. AIC
(6.957)*
(6.970)*
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Table 6. Model selection criteria for symmetric and asymmetric GARCH Model
GARCH Model
Selection criteria
GARCH
AIC
SIC
HIQ
AIC
SIC
HIQ
AIC
SIC
HIQ
AIC
SIC
HIQ
AIC
SIC
HIQ
AIC
SIC
HIQ
BIC
GARCH-MEAN
EGARCH
TGARCH
PGARCH
CGARCH
Normal
6.976
7.023
6.995
6.973
7.029
6.995
6.953
7.008
6.974
6.978
7.034
7.000
6.969
7.034
6.995
6.970*
7.035*
6.995
2496.413
Student’s-t
6.962*
7.017*
6.983*
6.958*
7.023*
6.983*
6.942*
7.007*
6.968*
6.962*
7.027*
6.987*
6.957*
7.031*
6.986*
6.974
7.057
7.000*
Error Distribution Assumptions
Generalized
Student’s-t(v=3)
6.970
7.001
7.025
7.047
6.992
7.019
6.967
6.996
7.032
7.052
6.992
7.018
6.950
6.989
7.015
7.045
6.976
7.011
6.972
7.001
7.036
7.056
6.997
7.023
6.965
7.005
7.039
7.065
6.994
7.026
6.967
7.035
7.041
7.100
6.996
7.061
Generalized (v=3)
7.063
7.109
7.081
7.063
7.119
7.085
7.028
7.084
7.050
7.066
7.121
7.088
7.057
7.121
7.082
7.045
7.110
7.070
MinSIC
Overall Min
SIC
(6.962)
(6.958)
(6.942)*
6.942 *EGARCH in
Student’s-t
(6.962) *
(6.957)*
(6.970)*
(249.4163)
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The variance Equation:
Log (GARCH)= -0.089
0.089 + 0.537
t21
0.096 t i 0.919 log t2 j
2
t 1
t 1
(0.502) (0.000)
(0.111)
(0.000)
Schwarz Information Criteria (SIC) = 6.942
Results for Model Diagnostic Check are presented in Table 7, Fig.
Fig 6 and Table 8.
3.2 Heteroskedasticity
roskedasticity test for model fitness
Table 7 contains the results of the Heteroskedasticity Test to confirm the Fitness of the selected GARCH
Model. The below results revealed that from the null hypothesis for the test of ARCH there is no ARCH
effect should be accepted even at the 5% level of significance while the alternative hypothesis of ther
there is
ARCH effect should be rejected.
Table 7. Heteroskedasticity test for the best fitted GARCH family model
Models
EGARCH(1,1) in student’s-t Error
Distribution
Heteroskedasticity Test: ARCH
F-statistic
Prob. F((5,431,10,421)
n*R2
X2(5,10)
Lag 5
0.962097
4.823617
0.4407
0.4378
Lag 10
0.644732
6.515986
0.7753
0.7702
3.3 Correlogram Q-statistics
atistics test for model fitness
Fig. 5 shows serial test correlation using Correlogram Q-statistics
statistics in order to validate the fitness of the
model selected. Since the calculated probability values are greater than that of the standard probability value
(0.05),then the null hypothesis for test correlogram Q-statistics
Q
ternative is rejected
is accepted while the alternative
and this mean that the estimated model is confirmed to be appropriate.
Q
Test for fitness of the model
Fig. 5. Correlogram Q-statistics
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3.4 Normality Test
Table 8 shows the results of descriptive statistic test for normality. This is done to know whether the model
obtained follow a normal distribution order. From all indicators the results show that the hypothesis of
normality should be rejected while the alternative hypothesis should be accepted. This means that the model
is not normal.
Fig. 6 shows the Quantile Plot for Normal Distribution and Quantile of EGARCH Model in student’s
Distribution. In the graph below in Fig. 5, lie on a straight line which reveal that the residual follows a
standardized order of a normal distribution
Table 8. Descriptive statistic normality test
Mean
Median
Max
Min
-0.0070
0.0105
3.3886
-2.5325
Std.
Dev.
0.7564
Skewness
Kurtosis
-0.3626
4.1891
JarqueBera
35.726
P-value
0.000
3
Quantiles of Normal
2
1
0
-1
-2
-3
-3
.
-2
-1
0
1
2
3
4
Quantiles of EGARCH
Fig. 6. Quantile plot for normal distribution and quintile of EGARCH Model in student’s distribution
4 DISCUSSION
The descriptive statistics in the Table 1 as reported from the result of the analysis reveals a positive mean
value of 0.123, indicating that the data series have positive mean-reverting. This means that at a certain level
of volatility, the data, when subjected to constraint, will return to its favourable position [14]. Also, the
standard deviation is 8.909, which is simply referred to as the risk measure associated with the series under
investigation. The result also confirmed that the returns on the crude oil price series is negatively skewed
with the value (-0.092) which means that the left tail of the distribution was longer indicating that the mass
of the distribution was shifted to the left. Meanwhile, the distribution Kurtosis is reported to be 5.535, which
means it is greater than the kurtosis of a normal distribution. This also that it is leptokurtic and has a flatter
tail. This is a standard characteristic behaviour mostly exhibited by financial assets. Also, the Jarque-Bera
test statistic gives the value 119.210 with a corresponding probability value of 0.000 confirming that the fact
that the data is not normally distributed. Therefore, for the data to satisfy this condition, it means that the
null hypothesis of normality would be rejected while the alternative of non-normality should be accepted.
According to Abdulkaremet al. [15], this is one of the conditions to be satisfied before we can apply an
alternative inferential statistic like the GARCH and Markov-Switching GARCH model. The result reported
from the estimated descriptive statistics test corroborates Deebom & Essi's [11] result. In modelling price
volatility of Nigerian crude oil market between 1987 and 2017 using the Generalized Autoregressive
Conditional Heteroskedasticity (GARCH) model. The result presented in this study also agrees with
Moujieke and Essi's (2019) findings in modelling returns on prices and sales of crude oil between 1997 and
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2017 using the GARCH model. The result of this present study also confirms Minoo and Shahram [16]
findings in comparing regime-switching GARCH models and GARCH models in developing countries (a
case study of Iran). The data is also fitted to an Autoregressive Moving Average (ARMA) model, the
estimation was done to obtain the residual for the test of volatility clustering and ARCH effect. The result
reported in the model (4.1) confirms that the ARCH component in the model was significant at 5 per cent
level of significance. However, the residual obtained from the estimation, as in Fig. 2 as the plot of return on
monthly crude oil prices (Dollar/Barrel) confirmed the presence of volatility clustering. Meanwhile, the
result in Table 2 also indicates evidence of the existence of ARCH effect. We notice that the number of
observations (n) multiplied by the coefficient of regression (R2), i.e. (nR2) was higher than the probability
value of the chi-square (X2) distribution. Therefore, it was confirmed that the null hypothesis which states
that there is no presence of ARCH effect should be rejected, and the alternative hypothesis that there is
ARCH effect, be accepted. The result reported here concerning the test for ARCH effect agreed with Cruicui
and Luis [17] findings in risk modelling in the crude oil market: a comparison of Markov-switching and
GARCH models. In Cruicui and Luis [17], it was found that the coefficient of the regression model
multiplied by the number of observations (nR2) was more significant than the probability value of the chisquare (X2) distribution satisfying the presence of ARCH effect. Results obtained here is also in line with
Veysel and Caner [18] findings in estimating the impact of oil price volatility to oil and gas company stock
returns and emerging economies. In Veysela and Caner [18], it was observed that there is the presence of
heteroskedasticity before GARH models used to fit the model in the study. This confirmed Abdulkarem and
Abdulkarem [15] assertion about when to apply the GARCH model in estimating a financial data series.
Abdulkarem and Abdulkarem [15] asserted that before GARCH model can be fitted to financial data series,
there must be the presence of ARCH effect which is one of the key conditions that GARCH model used in
removing ARCH during the process of estimation.
Table 3 contains results reported from the analyses of standard GARCH model with their direct error
distribution assumptions which include; normal, student's –t, generalized, student's–t with a fixed degree of
freedom (V=3) respectively. As it was reported in Table 3, co-efficient of ARCH (1) model is significant at
5 per cent level of significance in all the GARCH (1,1) models which suggest that the present returns on
crude oil prices are predicted by its past return. The positive coefficient of (0.167) in normal (0.179) of
(student ‘s–t), (0.177) (generalized), (0.198) (students with fixed degree of freedom V =3) and (0.143)
(generalized with fixed degree of freedom) error distribution shows that current return will be 16.7%, 17.9%,
17.9%, 17.7%, 19.8% and 14.3% respectively more than the previous months return. Similarly, in the
variance equation, the ARCH (1) model are all significant at 5% level of significance. This indicates that the
previous month's innovations are capable of explaining the current volatility. Also, the positive coefficient of
ARCH in all the variance equation shows that this month volatility will be higher. However, the estimation
of the GARCH (1,1) process also accounts for past period volatility in the analysis of these months'
volatility. These models captured the persistence of last period volatility. It merely means that these months’
conditional volatility is majorly governed by prior month’s innovations of the ARCH term as well as
previous period volatility (GARCH) condition. The degree of volatility persistence in all the model with
respect to their corresponding error distribution assumptions are in the following ascending order of
magnitude, and they include; GARCH (1,1) in generalized error distribution with fixed degree of freedom
(V=3) having volatility persistence of (0.746) as the highest, followed by GARCH (1,1) in student's –t with
fixed degree of freedom (V=3) (0.716), next was GARCH (1,1) in normal error (0.604), GARCH (1,1) in
generalized error (0.574) and GARCH (1,1) in student' s-terror distribution (0.543). In all, this means that
the estimator that has the highest volatility persistence was GARCH (1,1) in generalized error distribution
with a fixed degree of freedom (V=3). However, from the result reported in the analysis, it then means that
the previous month's crude oil price information has an impact on this next month returns which has 74.6%,
71.6%, 60.4%, 57.4% and 54.3% volatility respectively of last month transfers to the next month.
Comparing the five models on the basis of their fitness and performance with respect to the basic two
common selection criterion (AIC and SIC), then GARCH (1,1) in student's-t distribution has the least Akaike
and Schwartz information criterion. Therefore, the GARCH (1,111) model in student's –t distribution
outperforms the other models. GARCH (1,1) in Mean (GARCH-M) distribution was also estimated, and the
results were reported in Table 3, as shown in chapter four of this study. According to Deebom and Essi [11],
this model measure perceived risk and perceived risk mostly account for on higher return on the average of
the overall estimation. However, Table 3 as reported shows that all the ARCH (α) terms in the mean
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equations are significant at 5% level of significance which suggests that last month's returns on crude oil
prices in the crude oil market are predicted by this month volatility. It was also implied that 1 per cent
increase in this present volatility causes 16.28%, 17.24%, 17.24%, 18.56% and 14.607% respectively as
shown in the result as an increase in these current month crude oil prices returns. Also, it was reported from
the results of the analysis that all the co-efficient of the GARCH terms have positive signs, and they are all
significant at 5% level of significance. This means that the risk premium parameters (0.639, 0.688, 0.666,
0.736 and 0.580) determine these months’ conditional volatility. Also, confirmed the fact that in all the
estimated models and the volatility of crude oil prices is capable of providing the much need information on
the series returns. However, the degree of persistence and volatility of impact were estimated as follows:
GARCH (1,1) - mean in generalized error distribution with a fixed degree of freedom (V=3) has the highest
volatility persistence of (0.740) , follow by GARCH (1,1) -mean in student's –terror distribution with fixed
degree of freedom (V=3) (0.718), next was GARCH (1,1)-mean in normal error distribution assumption
(0.600), also, GARCH (1,1)- mean in generalized error with volatility persistence of (0.571) was the next
and the last but the least model was GARCH (1,1)-mean in student's –t error distribution with persistence
volatility of (0.539). This simply means that the percentage of their impactis74.0%, 71.8%, 60%, 57.1% and
53.90% respectively comparing the five models on the basis of fitness and performance with respect to the
basic two common selection criterion (AI &SIC), GARCH (1,1)- Mean in student' s-t distribution has the
least Akaike and Schwartz information criterion, therefore, GARCH (1,1) –mean model in student' s-t error
distribution outperforms the other models.
Table 4 contains the results of the analysis of standard asymmetric GARCH (1,1) models as reported from
the three classes of the asymmetric GARCH models estimated in the study. The first model on the table was
the Exponential Generalized Autoregressive conditional Heteroskedasticity (EGARCH) models of order 1.
According to Vina, Abdul and Bezon [19], this model accounts for asymmetric responses of conditional
variance to all kinds of shocks, and this is determined by the magnitude as well as the sign of news (which
could be positive or negative). In all the estimated models, ARCH in the mean equations shows that they all
have positive co-efficient (0.191, 0.199, 0.195, 0.214 and 0.195) and they are all significant at the 5 per cent
levels of significance. This means that there is no leverage effect as it was suggested in Vina et al. [19]. In
Vina et al. [19], it was suggested that when ARCH co-efficient in a GARCH model has a positive sign, and
it is significant, it means that the positive leverage effect is not effective and it does not have any significant
effect on the system. Similarly, all the asymmetric co-efficient have negative signs, but they are significant
at the 10 and 5 per cent level of significance, respectively. Also, it was confirmed from the results of the
analysis as it was reported in this study that all the asymmetric co-efficient (-0.007, -0.096, -0.776 and 0.125) were less than zero and this simply means that negative shocks increases as estimated the increased
volatility is more than positive shocks of the same magnitude. The degree of volatility persistence in all the
models estimated with their corresponding error distribution assumptions are in the following ascending
order of magnitude, and they include; EGARCH (1,1) in normal error distribution (108.9%) as the highest
followed by EGARCH (1,1) in student's–t distribution (1.118%), next was EGARCH(1,1) in generalized
error distribution (110.3%), EGARCH (1,1) in student' s-t with fixed degree of freedom (116.0% and
EGARCH (1,1) in generalized error distribution with fixed degree of freedom (V=3) (106.4%).This means
that the model with the highest volatility persistence was EGARCH (1,1) in normal error distribution.
However, from the results reported from the analysis, it then means that the persistence of past volatility
explained the current volatility of persistence. Comparing the five models estimated on the basis of their
fitness and performance efficiency EGARCH (1,1) in student's –t was considered the best since it has the
least Akaike and Schwartz information criterion. From the results obtained using EGARCH (1,1) models
with their corresponding error distribution, it was found that the larger the size of the estimated news
components, the negative news revealed were highly associated with greater volatility. Conditional volatility
also was discovered to have asymmetric characteristic behaviour which was prone to good news sensitivity.
This finding corroborates Vina et al. [19] assertion in estimating financial forecasting power of ARCH
family model: a case of Mexico. The results obtained here agree with Charan et al. [20] studied in Modelling
Stock Indexes Volatility: Empirical Evidence from Pakistan Stock Exchange. In Charan et al. [20] studied it
was found that EGARCH or GARCH models are the best fit for all the series as decision making criterion
Akaike information criterion (AIC) and Schwarz criterion (SC) are least in these models.
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In another development, Threshold Generalized Autoregressive Condition Heteroskedasticity (TGARCH)
models were also estimated in the study. According to Vina et al. [19], the TGARCH (1, 1) models account
for impacts of good or bad news on the conditional volatility by introducing a dummy variable. The results
obtained revealed shows that ARCH coefficients of all the estimated models show the present of bad news
(since Yi < 0 i.e 0.175, 0.196, 0.188, 0.219 and 0.147) and the asymmetric co-efficient (such as 0.124, 0.162,
0.133, 0.287 and 0.104) are all less than zero. Also, they are not all significant at 5% level of significance,
and so, this suggests that leverage effect is absent. It also means that bad news does not increase volatility
existence. In like manner, the co-efficient of the GARCH is significant at the 5% level of significance, and
so, these suggest that the past month's variance have no impact on the conditional volatility of these present
months. The speed of reaction of volatility to market shocks could be rated as thus; 65.65%, 71.89%,
68.76%, 77.32% and 58.75% respectively. Also, Power Autoregressive Conditional Heteroskedasticity
(PARCH) models were also estimated in the study and according to Omorogbe and Ucheoma [13], the
power Autoregressive Conditional Heteroskedasticity (PARCH) models also measures leverage and
asymmetric effects. The results obtained from the analysis shows that all the coefficients of the ARCH,
asymmetric and GARCH terms were all significant at the 5% levels of significance. This means that the
speed of reaction of the conditional variance in the crude oil market is high and volatility persistence is high.
The degree of persistence as reported from the results of the analysis are given as, 95.6%, 115.8%, 109.67%,
139.38%,and 59.83% respectively. This means that the model with the highest volatility persistence was
PARCH (1,1) in Students’-terror distribution with fixed degree of freedom (v=3). However, from the results
reported from the analysis, it then means that the persistence of past volatility explained the current volatility
of persistence. Comparing the five models estimated on the basis of their fitness and performance efficiency
PARCH (1,1) in student's –t was considered the best since it has the least Akaike and Schwartz information
criterion (6.957 and 7.031) respectively. The results obtained here agree with Alhassan and Abdulhakeem
[15] findings. In Alhassan and Abdulhakeem’s [15] analyzed oil price –macroeconomic volatility in Nigeria
and from the results of the study, it was found that there is persistence volatility in PARCH (1, 1) in
students’-t. Although, the little variations in the two studies is that the present study confirmed that
persistence volatility occurs in PARCH (1, 1) in students’-terror distribution with fixed degree of freedom
(v=3) whereas the formal found in PARCH (1, 1) in students’-terror distribution not with fixed degree of
freedom at v=3. Component GARCH (CGARCH) Model was also estimated in the study and according to
Omorogbe and Ucheoma [13], considered volatility as the time vary in the long-run. The results obtained
from the analysis shows that all the coefficients of the ARCH, asymmetric and GARCH terms were all
significant at the 5% levels of significance. This means that both ARCH and GARCH terms representing
Short‐run and Long run persistence are significance. The degree of persistence as it was reported from the
results of the analysis were given as, 158.18%, 156.67%, 161.54%, 179.94%,and 145.31% respectively. This
means that the model with the highest volatility persistence was CGARCH (1,1) in students’-terror
distribution with fixed degree of freedom (v=3) (179.94%) and comparing the five models on the basis of
fitness and performance with respect to the basic two common selection criterion (AIC and SIC) CGARCH
(1,1) in normal error performance best. The results obtain from this findings was synonymous with
Omorogbe and Ucheoma(2017) studied in the application of asymmetric GARCH models on volatility of
Banks Equity in Nigeria’s Stock Market.In Omorogbe and Ucheoma(2017) studied, it was found that
CGARCH (1, 1) in students’-terror distribution outperform others. The little variations in the two studies is
that the present study confirmed that persistence volatility occurs in CGARCH (1, 1) in students’-terror
distribution with fixed degree of freedom (v=3) whereas the formal found in CGARCH (1, 1) in student’sterror distribution. Although, the formal studied by Omorogbe and Ucheoma [13] on volatility of Banks
Equity in Nigeria’s Stock Market whereas this study was done in crude oil market. The result in Table 6
contain model Selection Criteria for both symmetric and asymmetric GARCH Model on the basis of AIC,
SIC and HQ. However, the final result was restricted to model with the least Schwarz criterion (SIC). This
was done because Schwarz criterion (SIC) penalized models for loss of degree of freedom. Therefore, From
the results obtained it was found that the overall best fit model for decision making using Schwarz criterion
(SIC)was the EGARCH in student’s – t error distribution assumption. The decision obtains concerning
model with the least Schwarz criterion (SIC) in this study agree with the following studies; Charan, et al.
[20] studied in Modelling Sectoral Stock Indexes Volatility: Empirical Evidence from Pakistan Stock
Exchange. In Charan et al. [20] studied, it was found that EGARCH or GARCH models are the best fit for
all the series as decision making criterion Akaike information criterion (AIC) and Schwarz criterion (SC) are
least in these models. Also, the findings of the study corroborate Deebom and Essi’s [11] findings in
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
modelling price volatility of Nigerian crude oil markets between 1987- 2017 using Generalized
Autoregressive Conditional Heteroskedasticity (GARCH) model. In Deebom and Essi’s [11], after
comparing the results of both symmetric and asymmetric GARCH it was found that first order symmetric
GARCH model (GARCH, (1,1) in student’s-t error assumption gave a better fit than the first order
Asymmetric GARCH model (EGARCH (1,1)) in Normal error distributional assumptions. Similarly, this
present study is also similar to Moujieke and Essi’s [21] study on modelling Returns on Prices/ Sales of
Crude Oil Using GARCH Model between1997-2017. In Moujieke and Essi’s [21] study, it was found that
first order symmetric GARCH model (GARCH, (1,1) in generalized error distribution with fix degree of
freedom gave a better fit while in the first order Asymmetric GARCH model, the EGARCH (1,1) in normal
error distributional assumptions gave a better fit. However, comparing the two classes of the models on the
bases of their fitness the EGARCH (1, 1) in normal error distributional assumptions gave an overall best
fitness. After estimation, there is need to do several models diagnostic and performance confirmatory test.
This will enhance the study to be sure that the model is okay, reliable in terms of performance efficiency and
predictability. Therefore, the selected model was subject to the following model diagnostic and performance
confirmatory and this include, heteroskedasticity test for model fitness, Correlogram Q-statistics test for
model fitness, Normality Test and Quantile Plot [11]. From the findings of the study, heteroskedasticity test
for model fitness revealed that there is no ARCH effect and this mean that it is does not violates the
homoskedasticity assumption for line model [22]. In Gujerati [22] textbook titled Basic Econometrics, it is
clearly stated in basic econometrics that any model that violates the homoskedasticity assumptions suffered
from heteroskedasticity problems and this can be eliminated using the GARCH models. This result reported
from this estimation agrees with Deebom and Essi [11] and Moujike and Essi [11]. The result obtained for
model fitness using Correlogram Q-statistics test in this study also agree with Atoi [23] findings using Q-Q –
plot. Similarly, Normality and Quantile Plot were all in line with Abduikareem and Abdulhakeem [15]
recommendation in analyzing oil price – macroeconomic Volatility in Nigeria. In Abduikareem and
Abdulhakeem [15] it was recommended that in examining GARCH models that it is necessary that
normality and Quantile Plot validated to be sure that the model are well fitted.
5 Conclusion
Based on the results the asymmetric behaviour of the data, the study applied EGARCH, GJR-GARCH,
PARCH, and CGARCH models, so that it can investigate if there is a various effect of good and bad news
on the future volatility in crude oil price dynamics. However, much emphasis was on EGARCH model since
it was considered best fit and an appropriate model. Therefore, the expected outcome for the existence of
asymmetric effect in the data was related to the estimated gamma (γ) co-efficient of the model to have
negative significant, and since the results in this study was positively significant this shows that; there is no
support to the existence of leverage effect in crude oil price dynamics. Thus, crude oil price dynamics return
was considered to be volatile. Hence, whether there is good news (positive)or bad news (negative), shocks
are of the same magnitude, they will have the same impact on the future volatility. The results of this
findings in particular is consistent with few studies in regards to detecting the asymmetric effect in the data,
the study applied EGARCH (1, 1) model, so that it can investigate if there is a various effect of good and bad
news on the future volatility in Amman Stock Exchange (ASE). Therefore the expected outcome for the
existence of asymmetric effect in the data is related to having negative significant gamma (γ) and since the
results in our study is positively significant this indicates that; there is no support to the existence of leverage
effect in Amman Stock Exchange. Thus, the stock return is considered to be volatile. Hence, whether the
shocks are positive (good news) or negative (bad news) of the same magnitude, they will have the same
impact on the future volatility.
6 Recommendations
Considering the level of risk associated with trading commodity like crude oil in foreign markets with its
corresponding prices return series, investors, financial analysts and Government should observe the
following recommendations:
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Dum et al.; ARJOM, 17(3): 35-54, 2021; Article no.ARJOM.68132
1.
2.
3.
Financial analysts, investors, and those doing empirical studies, given the level of risk associated with
the returns and other investment, should consider variants of GARCH models with alternative error
distributions, for example fixed degree of freedom with parameter (v=3) for robustness of results.
Also, investors, Marketers and Government that wants to invest in crude oil and its constituents as
lucrative business option should do so base on the advice of an empirical result of a GARCH model
with the lowest AIC and SIC as in the case EGARCH model in this study. This is because EGARCH
model recommends that when there is low leverage effect its means that investing in such sector will
rely on the value of the shares issued by an oil producing company as a way to attract the investors to
invest in crude oil business in order get more returns with lesser risks.
The study also recommends an adequate regulatory effort by the highest financial institution in the
country like the Nigeria central Bank over currency operations to enhance efficiency of markets
performance and reduce volatility aimed at boosting investors’ confidence in foreign trading
operations.
COMPETING INTERESTS
Authors have declared that no competing interests exist.
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