Volatility Forecasting of Crude Oil, Gold, and Silver Futures:
A Case of Pakistan Mercantile Exchange
SHAMSUL NAHAR ABDULLAH1, IQRA KHAN2, FARAH NAZ2, KANWAL ZAHRA3,
TOOBA LUTFULLAH2
1Faculty of Business and Communication,
INTI International University,
Nilai,
MALAYSIA
2Department of Accounting and Finance,
Kinnaird College for Women,
Lahore,
PAKISTAN
3Faculty of Management Sciences,
University of Central Punjab,
Lahore,
PAKISTAN
Abstract: - The volatility of commodity prices has been a topic of interest for researchers and investors for decades.
In recent years, the prices of key commodities have shown significant fluctuations, causing challenges for market
participants to make informed investment decisions. Therefore, this paper provides an understanding of forecasting
and modeling the volatility of commodity futures in the Pakistan Mercantile Exchange (PMEX) using GARCH and
ARIMA models. The study aims to analyze and predict the volatility of three key commodities, namely Gold,
Silver, and Crude Oil, and to compare the performance of the two models in forecasting their future prices. The
study uses daily time-series data from 2010 to 2021 and finds that the prices of Gold and Crude Oil futures exhibit
asymmetrical effects on their volatilities, while silver futures show stability over time. The results are useful for
potential investors, economic agents, managers, financial researchers, and policymakers to analyze the volatility of
commodity futures in the market. This will also help the investors to diversify their investments by analyzing the
variation in such commodities in the international markets.
Key-Words: - ARIMA, GARCH, PMEX, GOLD futures, crude oil futures, volatility
Received: April 11, 2023. Revised: September 27, 2023. Accepted: October 2, 2023. Published: October 13, 2023.
1 Introduction
Forecasting volatility is critical for financial analysts
to examine the significant impact on the global
economy and individual economies, [1]. It enables
the analysis of various macroeconomic variables that
depend on volatility factors. Financial markets trade
in commodities that are valuable assets for investors,
such as futures contracts. Therefore, derivative
markets are highly volatile, which increases their
risk. In these markets, forecasting is crucial,
especially for highly volatile commodities like gold,
silver, and crude oil. This price fluctuation can cause
volatility spillover where the volatility of different
commodities is interconnected, [2]. As a result,
market participants must be well-informed about
future uncertainties to make effective investment
decisions. Financial researchers and investors have
emphasized in-depth analysis of forecasting
techniques in recent years to avoid the negative
repercussions associated with future price
uncertainty, [3]. Accurate forecasting can predict
future uncertainties and prevent risky investments.
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Forecasting the volatilities of various commodities
plays a substantial role in the current era, where
researchers must choose an efficient model to
forecast data and identify any uncertainties related to
it, [4]. Therefore, efficient analysis can be made
using certain forecasting techniques like GARCH
and ARIMA, which are widely used to predict
macroeconomic variables, [5]. Several studies have
used these models to predict volatilities and have
compared them. However, the GARCH model is
more accurate in the long run. In [6], the authors
studied the comparison between the GARCH and
ARIMA models for forecasting gold prices in
Malaysia. The results found that the GARCH model
was a more efficient model for forecasting prices
than the ARIMA model. Crude oil is at the top of the
traded items list in the world which has
approximately 10% in the global trade volume due to
the rise in its volatility prices over the past 30-40
years, [7]. Crude oil covers two-thirds of the world’s
energy demand, and its trade is conducted through
various contracts, including spot prices and futures,
[4].
Gold is a highly significant commodity in
international trade. In 2008, following the recession,
the price of gold experienced a 6% increase
internationally, while the prices of other minerals
decreased, and a 40% decline was recorded in the
equity market. The study, [8], concluded that the
behavior of gold prices does not correlate with the
variations in other markets, and it behaves differently
compared to other markets. Therefore, to analyze the
volatility of such commodities, this study examined
the Pakistan Mercantile Exchange (PMEX). In 2007,
PMEX was established as the National Commodities
Exchange of Pakistan and has since been extended to
three digits. PMEX solely has all rights in dealing
with the future markets of key commodities and is
operated under the Securities and Exchange
Commission of Pakistan (SECP), [9].
PMEX is a highly advanced and well-structured
institution that has implemented efficient techniques
to meet the demands of modern exchanges. Its robust
infrastructure enables PMEX to offer a wide range of
services, including commodity trading, trusteeship,
and clearing. With a membership of 326, PMEX
handles an average daily volume of 5 billion PKR.
The international membership of PMEX includes
prestigious organizations such as Dubai's Gold and
Commodities Exchange (DGCE), with whom they
have signed Memorandums of Understanding
(MoUs), [10], along with partnerships with the Iran
Mercantile Exchange, Association of Futures Market
(AFM), Borsa Istanbul, Futures Industry Association
(FIA), Izmir Commodities Exchange (ICE),
Hungary, and USA.
Initially, PMEX primarily focused on gold futures
trading. However, in 2009, the Exchange introduced
crude oil as a futures contract, [11], which has now
become a prominent commodity traded on the
platform. Alongside crude oil, silver and gold are
considered the major products traded on the
Mercantile Exchange of Pakistan.
This study makes a significant contribution in two
aspects. First, it compares the models that can help in
forecasting the future of commodities, and among
them, the GARCH and ARIMA models are
considered on top in predicting the futures of crude
oil, silver, and gold. While previous literature has
applied various statistical methods to analyze gold
prices, this research focuses on utilizing the GARCH
and ARIMA models to estimate and analyze the most
recent future price results using current data. Second,
the study also targets to capture the recent impact of
the COVID-19 pandemic and major political or
economic shocks on the volatility of the selected
commodities by identifying a significant time-
varying jump in the data. Previous research has also
attempted to capture the effect of such jump
behaviors in studying and forecasting volatility, [12],
[13]. The study will add great credibility to the
commodity market for investors, policymakers,
government, and financial researchers in Pakistan.
While many studies focus on forecasting a single
commodity, the contribution of this study is to
include three dominant commodities and perform
simultaneous forecasting of these three dominant
commodities traded on the Mercantile Exchange of
Pakistan: crude oil, gold, and silver. The forecasting
for these three major commodities is performed
through the two famous models of volatility
prediction i.e., ARIMA and GARCH models.
The structure of this paper is as follows. Section 2
reviews the prominent research and literature support
that emphasized the forecasting and modeling of
futures price volatility of the commodity market.
Section 3 includes the description of the selected
method used for the analysis of this research. While
Section 4 illustrates the gold, crude oil, and silver
futures prices time series from the PMEX database
and presents its results produced by forecasting
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models GARCH and ARIMA. The conclusion of this
research is drawn by section 5.
2 Literature Review
There is a vast amount of existing literature that
covers the issue of volatility in the futures of key
commodities in the financial assets that are being
traded at stock exchanges and mercantile exchanges.
Accurate forecasting related to volatility can not only
prevent negative returns but can also provide an
opportunity for the participants of the financial
markets to gain huge positive returns as well. This
study made a significant contribution in the finance
domain because accurate forecasting would be of
tremendous help to investors to manage their risk,
select profitable portfolios, price the derivatives
precisely, devise viable economic policies and
formulate hedging techniques. Economic stability is
significantly affected because of the existence of
volatility in the prices of crude oil, [14]. The
macroeconomic aspects can impact the future
volatility in the stock exchange markets of the
country leading to infer long-term effects, [15]. The
study, [16], identified various issues related to the
uncertain behaviors of crude oil prices and concluded
that these uncertainties caused the economic
recession of 1980 and 1982. Similarly, [17], [18],
[19], [20], studied that crude oil prices can cast a
significant influence, internationally, on different
macroeconomic factors, for example, inflation, GDP,
stock market performance, and exchange rate.
However, [21], analyzed the relationship among
silver, gold, oil, and energy sectors which depicts the
positive dependence of energy uncertainty and crude
oil prices in the medium and long run. Looking at the
significance of forecasting in the financial world,
vast literature exists on the topic. The studies aim to
determine the most appropriate technique for
forecasting volatility in asset prices. Some of the
significant literature regarding the techniques of
forecasting used in the financial world have been
discussed as follows: [22], applied the GARCH
family models on the electricity prices to capture
volatility in the deregulated market of California.
They ultimately concluded that GARCH performs
comparatively better than ARIMA. The study, [23],
referred to the involvement of the hedging concept to
analyze the volatility of gold through the GARCH
model and its impact to provide a better view to the
investors. The volatility in the gold market may
expose the risks for the currency of a country,
however, it can protect the investor against the
currency risks, [24].
Various studies have forecasted the volatility
persistence in the equity market and foreign
exchange market. However, very few studies have
investigated the persistence in the prices of oil in
international markets. The term persistence is often
specifically referred to the GARCH models, where
conditional variances shock increased to excessively
high rates which are comparatively lower than
exponential rates caused by decays in the shocks,
[25], [26], [27]. Whereas, [2] found that the volatility
models CGARCH and FIGARCH are more efficient
in capturing persistence in the oil markets of Texas,
Brut, and Dubai as compared to GARCH and
IGARCH. The study, [28], elaborated on the research
study of, [2], but the results of both studies varied
considerably. Unlike previous findings, this study
found that not a single model outperformed the loss
function, but in general, results showed that the
nonlinear model of GARCH is a comparatively more
accurate predictor than that of the linear model. The
spillover effect of gold may affect the performance
which affects the analysis of the institutional
investors to gain more returns however, the
performance can be identified using the
methodologies such as the GARCH model that
provides more accurate predictor results, [29], [30].
The study, [31], analyzed the Chinese investors’
sentiments and their impact on the volatility forecast
of the prices of crude oil, gold, and silver. The study,
[32], approached the time domain spillover method
to investigate the connection between the crude oil
prices and stock indexes with the metal prices where
the results provide evidence that the stock index is
not a contributor towards price spillover.
The study, [33], used crude oil data from China
and analyzed the role of jump and leverage in the
prediction of realized volatility (RV), the results
revealed the useful effect of leverage and the
significant effect of a jump in predicting the long-
term information thereby leverage has the best
predictive power for the oil futures. The study, [34],
investigated the efficiency of various forecasting
models that includes GARCH, EGARCH, APARCH,
FIGARCH, and APARCH to forecast the volatility of
oil prices in eleven international markets over a span
of twelve years. APARCH performed better in
comparison to the other models in line with it.
Furthermore, the study stated that conditional
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standard deviations predict prices more accurately
than those conditional variances. The study, [35],
conducted a study by making a comparison between
the models of GARCH & ARIMA for forecasting the
gold prices of Malaysia. The study concluded that the
GARCH model is a comparatively more efficient
model to forecast prices than the ARIMA model.
Few of the studies figured out that the combination
extensions of ARIMA models and GARCH models,
particularly the FIGARCH and ARFIMA models, are
identified as accurate estimators for accessing the
influence of market instability on the volatility and
returns of various commodities, [36], [37], [38], [39],
[40]. Whereas, [10], modeled and forecasted the
market risks and the conditional volatility of highly
volatile commodities such as natural gas, silver,
crude oil, and gold by the GARCH family models.
The results revealed that the non-linear models of
GARCH can more efficiently forecast the volatility
of all these commodities compared to the other
available methods. FIPARCH, an extension of the
GARCH model, is identified as more accurate for
predicting the volatilities in both the long and short
run. Oil is one of the commodities that are most
important in international trade therefore accessing
its volatility is always a top priority task of investors,
[1], [41].
Getting accurate estimates regarding the volatility
of oil prices can not only help policymakers to hedge
their foreign exchange risk, rather it can add
tremendous economic stability, [42]. A wide array of
studies has been conducted in this field. Like, [43],
studied the influence of uncertainty in oil prices on
the manufacturing industry of the South African
region by using the model of GARCH. The study
concluded that uncertainty in oil prices could
negatively affect the manufacturing sector of South
Africa substantially. The study, [44], investigated the
significance of gold and crude oil on the stock market
index of Pakistan which depicts the insignificant
relation of oil towards the index as compared to gold
which showed significant relation to the market. The
study, [37], demonstrated the phenomenon that the
reduction in the crude oil price of 1985 did not lead
to a significant increase in the output of the United
States due to the high level of uncertainty associated
with the crude oil price.
The study, [45], investigated that the market
participants and policymakers also have an important
role to reach the correct forecast in the stock market
of the United States where the volatility can be
analyzed effectively by using the information of
futures of key commodities. On the contrary, [46],
investigated that forecasts are not improved by
volatilities that are linked with the commodities and
thus no volatility spillovers can be detected using the
heterogeneous autoregressive (HAR) models. The
study conducted on the derivatives of oil prices is
done by, [4]. The study aimed to analyse and forecast
the volatility in the spot prices and future prices of
crude oil being generated by any political or
economic changes in Pakistan. The research used the
GARCH family models for the evaluation of
volatility in the prices of crude oil. The study
concluded that oil price derivatives tend to remain
volatile in the long run. The prices would increase
the shocks of a negative nature and would decrease
the shocks of a positive nature. Hence, the study
concluded that there is an impact of economic and
political changes on crude oil volatility.
Gold plays a key function in the international
financial sector and has long been utilized as a
measure of wealth and a method of income. Investors
usually use gold as a method to buffer inflation in
their portfolios due to its diversified portfolio, [28].
Previous research has extensively studied the
modeling of price volatility of key commodities,
using various frameworks and perspectives, yielding
valuable insights. However, the focus of these studies
has been limited to markets other than Pakistan,
leaving a gap in the literature regarding the analysis
of Pakistan's market. Additionally, while some
studies have examined the price volatility of
individual commodities, such as gold or oil, there is a
dearth of research that considers the price volatility
of all three commodities, including silver, to predict
their futures in Pakistan. This study aims to bridge
the existing gap by examining the price volatility of
gold, silver, and crude oil and predicting their futures
using appropriate modeling techniques in the context
of Pakistan's market and providing a comparative
analysis of ARIMA and GARCH models for
forecasting.
3 Data and Methodology
The primary objective of this research is to analyze
and forecast the volatility in the prices of three
significant commodities: gold, silver, and crude oil.
To achieve this objective, price data for these
commodities spanning from January 2010 to January
2021 has been collected from the derivatives market
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of Pakistan. The monthly data has been sourced from
the official database of the Pakistan Mercantile
Exchange (PMEX), which is known as a futures
exchange in Pakistan. This data not only allows for
the examination of volatility in commodity prices but
also facilitates an evaluation of the impact of the
COVID-19 pandemic on these prices.
Given the high volatility and fluctuations in gold
prices over time, both the heteroscedasticity approach
of ARIMA and the GARCH models are considered
suitable for testing the entire dataset. The ARIMA
model, a type of linear model, is capable of
representing both stationary and non-stationary time
series data, making it useful for prediction purposes.
On the other hand, the GARCH model specifically
tests for volatility in gold prices, capturing the
clusters present in the data resulting from pronounced
fluctuations over time. Therefore, both models will
be compared to assess their performance during the
period from January 2010 to January 2021.
Furthermore, this study aims to examine the
impact of the coronavirus pandemic on the prices of
crude oil, gold, and silver. To ensure the validity of
the time series models employed, the stationarity of
the selected variables is checked using the ADF unit
root test. Stationarity is a crucial assumption for most
time series models, including ARIMA and GARCH
models. If the data is found to be non-stationary,
these models cannot be effectively applied. Thus, it is
imperative to assess the stationarity of the data before
proceeding with the modeling phase.
3.1 The Box-Jenkins (ARIMA) Methodology
The ARIMA model is used for this research, which is
being introduced by Box and Jenkins, [47]. Thus, the
model is represented with the Box-Jenkins
methodology because it provides the efficient and
effective analysis and testing of forecasting
techniques for a univariate time period or the type of
data which involves the univariate series as it was in
our study, [48]. The major aim of the research was to
depict whether this model is suitable to effectively
test the volatility issues in commodities such as gold,
silver, and oil therefore the ARIMA model is tested
which is the generalized form of the Box-Jenkins
methodology, [49], [50]. The model tested with its
referred form as ARIMA(p,d,q) where the ‘p’ shows
the autoregressive order, ‘d’ required the integration,
and ‘q’ means the moving average parts involved in
the model. This referred to the form which helps in
testing the results for the time-series data because if
any term is missing or zero it will automatically
remove from the output results. For example,
ARIMA(0,0,1) results when the MA(1) model is in
the data, and on the other hand ARIMA(0,1,0) comes
when the I(1) model is in the data.
To predict the natural phenomena of different
types to utilize the modeling of the random process
an autoregressive (AR) model is better suitable where
the AR(p) denoted the order ‘p’ of the autoregressive
model. Hence, the AR (p) can be defined using the
equation:
The analysis of univariate time series models can be
analyzed with the moving average (MA) of the
ARIMA model with the order of ‘q’ and the notation
for this is referred to as the moving average model
MA (q):
The ARIMA model with the order (p, q) is defined
as:
The Box-Jenkin methodology helps in depicting
the generalized form of the ARIMA model where the
order of p, d, and q provides the non-negative
integers of the ARIMA model. This order refers to
the autoregressive, integrated, and moving average
parts to approach and analyze the time series
modeling with the methodology of Box-Jenkins
respectively.
The methodology of Box-Jenkins is an important
technique as compared to other methodologies and
helps in analyzing the performance of variables
selected for the forecasting model as compared to the
performance of the same variables in the past to
check the generalizability of the models under each
class, [51]. However, the strategies can be applied
which are mainly depicted with the four-step strategy
of identifying, estimating, and diagnosis for checking
and forecasting. Thus, the patterns of the time series
can b represented by the categories mentioned:
Autoregressive models (AR): It is a linear
function to provide the basis for the past
values of variables.
Moving Average model (MA): It is the linear
combination that provides the basis for past
errors.
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Autoregressive-Moving Average models
(ARMA): It is the combination of categories
mentioned in the above two points of AR and
MA, [52].
3.2 ARCH Model
The volatility clustering can be observed in the time
series data of financials. However, the big shocks in
these volatile clusters might follow the other big
shocks and the same goes for the small shocks that
are mainly known as the residuals. To effectively
assess the variances in these types of models, it is
necessary to consider the historical patterns and
model them accordingly. For this purpose, the
previous literature can help such as the
autoregressive conditional heteroscedastic (ARCH)
model proposed by, [53], to pattern such volatility in
the market. This model is dependent on the squared
errors with the error term of ‘t’ to analyze the
variances with the specification given below for
ARCH (1) as:
The big shocks in the time ‘t’ can be depicted with
the model of ARCH (1) to analyze the absolute large
values when the variances of such values are also
large.
To check the order ‘p’ in the ARCH (1) model, it can
be represented as:
Thus, the shocks in period ‘p’ can be analyzed
through the ARCH model because the shocks that are
older than period ‘p’ may not affect the volatility of
the current shocks in the market because the ARCH
model adjusts them in the results, [53].
3.3 GARCH Model
The GARCH model introduced by [54], commonly
named Generalized Autoregressive conditional
Heteroscedastic provides the extension to the ARCH
model discussed previously. This model helps in
analyzing the lagged squared error terms with its
lagged terms because error variances are regressed
under the processing of lagged squared error terms.
Thus, the equations mentioned provide the GARCH
model with the order ‘p’ and ‘q’ where the first
equation shows the conditional mean equation, and
the second equation shows the conditional variance
equation:
µ
==+
+
0,≥0,
With the above equations, the GARCH(p, q) can be
analysed as:
µ
==+
+β
0,≥0,
The GARCH model is named Vanilla in the
literature because it is commonly used for the
financial time series.
Most of the prominent research on forecasting
used the GARCH and ARIMA models, [4], [22],
[28], [55], [56]. An econometric model GARCH was
introduced by, [54], and is now widely utilized by
many researchers to forecast the prices of different
financial instruments. For estimating GARCH, the
initial step is the estimation of the best fit and
appropriate autoregressive model. A further step is
the estimation of autocorrelation for error terms. The
last step in GARCH modeling is analyzing the
significance level. ARIMA is an econometric term
introduced by Box Jenkins, that’s why this model is
often called the Box-Jenkin Method. This method is
used for predicting the time series data where the
data shows non-stationarity. So, In ARIMA, the
initial step is to make different series. By breaking
down the term ARIMA, the AR term is referred to as
an Auto-regressive term, I is referred to as the
differencing term and MA indicates the number of
moving averages, [57].
4 Empirical Results
This study employs GARCH and ARIMA models to
facilitate the forecasting process, specifically to
predict future prices of gold, silver, and crude oil. A
comparative analysis is conducted among the
selected models to determine the most suitable
approach for accurate price prediction.
Before commencing the modeling phase, the
volatility patterns within the datasets are visually
represented through graphical representations.
Additionally, the stationarity of the datasets is
examined to ensure reliable forecasting results.
To forecast the futures prices of gold, silver, and
crude oil, a comprehensive comparison is performed
between the GARCH and ARIMA models. The
objective is to identify the best-fit model that exhibits
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optimal performance in forecasting the volatility
associated with the futures prices of these
commodities.
The initial step in the analysis involves assessing
the stationarity of the data through unit root tests.
The p-values for all three datasets are found to be
less than 0.05, indicating that the datasets exhibit
stationarity at the level. Table 1 presents the results
of the unit root tests conducted for the silver, gold,
and crude oil futures datasets, confirming their
stationarity.
Table 1. Unit Root Test ADF
Variable
Unit root
Test
P value
Decision
Crude oil
On level
0.0314<0.05
Data is
Stationary
Gold
On level
0.0023<0.05
Data is
Stationary
Silver
On level
0.00433<0.05
Data is
Stationary
To proceed with GARCH modeling, the first step
is to examine the presence of ARCH effects by
conducting a heteroscedasticity test. This test is
performed on all three commodities, and the results
indicate that the p-values for all cases are below 0.05,
suggesting that the data exhibits homogeneity. Table
2 displays these findings.
Next, the analysis checks for serial correlation by
applying the Breusch-Godfrey LM test to the crude
oil, gold, and silver futures datasets. The results
reveal that the p-value is 0.00 for all three cases,
indicating the presence of serial correlation.
Fig. 1(a): Gold price series
Fig. 1(b): Silver price series
Fig. 1(c): Crude oil price series
The LM values (Obs*R-squared) are 20.124,
52.431, and 47.986, respectively, suggesting that past
values positively influence future values. Table 3
provides a summary of these results.
Furthermore, one advantage of utilizing GARCH
models over ARIMA models is that GARCH can
capture non-linear data patterns, while ARIMA is
more suitable for linear data.
Fig. 1(d): Gold return series
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Fig. 1(e): Gold return series
Fig. 1(f): Crude oil return series
Fig. 1: Graphical Representation of Authors'
Calculations showing Gold, Silver, and Crude Oil
Prices and Return Series
Figure 1(a) to Figure 1(f) illustrates the price and
line chart series of commodities, highlighting notable
fluctuations, particularly during the COVID-19
period in 2020. Specifically, the trend of crude oil
prices exhibits a downward trajectory during this
time, largely influenced by the impact of the
pandemic. The demand side analysis of the
commodity indicates that containment measures and
economic disruptions stemming from the pandemic
resulted in reduced production and mobility,
consequently leading to a substantial decline in
global oil demand, [58]. Furthermore, the figure
provides a clear representation of the daily log return
series of commodities futures, revealing significant
clusters that attest to the occurrence of volatility
throughout the year 2020.
Table 2. ARCH and LM Test Statistics
Commodity
ARCH
Breusch-Godfrey
LM Test
Crude Oil
Obs*R
Squared
20.124
Prob.
F(1,1099)
0.0062
Prob.
F(2,1098)
0.000
Prob.
Chi-
Square(1)
0.0049
Prob.
Chi-
Square(2)
0.0000
Gold
Obs*R
Squared
52.431
Prob.
F(1,1099)
0.0042
Prob.
F(2,1098)
0.0000
Prob.
Chi-
Square(1)
0.0003
Prob.
Chi-
Square(2)
0.0000
Silver
Obs*R
Squared
47.986
Prob.
F(1,1060)
0.0000
Prob.
F(2,1059)
0.0000
Prob.
Chi-
Square(1)
0.0000
Prob.
Chi-
Square(2)
0.0000
The uncorrelated time series exhibit serial
dependence as a result of the dynamic conditional
variance process. The Autoregressive Conditional
Heteroscedastic (ARCH) effects manifest in the time
series, introducing heteroscedasticity or
autocorrelation in the squared series. When assessing
the significance of these ARCH effects, Engle's
ARCH test is more suitable than the Lagrange
Multiplier Test.
Upon analyzing the results, it is evident that the
ARCH LM test provides compelling evidence for
rejecting the null hypothesis concerning the series of
commodity futures returns. The results demonstrate
significance at the 1% level, leading to the rejection
of the null hypothesis that suggests the absence of
ARCH effects. Consequently, this rejection signifies
the presence of ARCH effects within the mean
equation of the residual series.
To further measure the forecasting ability, this
paper estimates the forecasts that are within the
sample. This sample forecasting shows the
predictability power of the model. If there is a small
difference in the magnitude of actual and forecasted
value, then this results in good forecasting power.
However, for this case, the GARCH (1,1) shows
good results which can be evident from Table 3.
Based on the analysis, the GARCH model has
been identified as the most suitable model for Crude
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2023.20.196
Shamsul Nahar Abdullah, Iqra Khan,
Farah Naz, Kanwal Zahra, Tooba Lutfullah
E-ISSN: 2224-2899
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Volume 20, 2023
oil futures. This determination is based on several
factors. Firstly, the Akaike, Hannan, and Schwarz
values of the GARCH model are lower than the
corresponding values of the ARIMA model.
Additionally, the Durbin Watson statistic for the
GARCH model is closer to two, indicating a better fit
compared to the ARIMA model.
Table 3. Results of ARIMA and GARCH
Model
ARIMA
GARCH
CrudeOi
l
Coefficient
P
value
Coef.
P
value
AR(1)
-0.449
0.00
1.66
0.00
MA(3)
-0.334
0.00
0.13
0.13
Gold
AR (4)
0.158
0.02
0.68
0.01
MA(1)
0.542
0.00
-0.04
0.17
Silver
AR(2)
0.552
0.00
0.87
0.00
MA(2)
-1.000
0.99
0.38
0.00
Furthermore, the estimated results of the
GARCH model provide additional evidence
supporting its suitability. The p-value of 0.04, which
is less than the significance level of 0.05, indicates
the overall goodness of fit for the study. With a
sample size of 84 observations, the GARCH(1,1)
coefficient of 0.386 is highly significant, as
evidenced by its p-value of 0.000.
Conversely, the estimated results of the ARIMA
model suggest that it is the best-fit model for Crude
oil futures. This conclusion is based on the lower
values of Akaike, Hannan, and Schwarz criteria
compared to the GARCH model. Additionally, the
Durbin Watson statistic for the ARIMA model is
closer to two and smaller than the corresponding
value for the GARCH model. These findings are
summarized in Table 4, which provides a
comprehensive comparison of the GARCH and
ARIMA models.
Table 4. Selected Model based on Minimum
Criterion
Model
ARIMA
GARCH(1,1)
Crude Oil Futures
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
(1,0,3)
48.52934
49.06509
49.05757
2.107575
48.97884
49.09460
49.22538
2.962236
Gold Futures
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
(4,0,1)
48.42438
48.54014
48.47092
1.941293
48.44187
48.55762
48.48840
2.757628
Silver Futures
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
(2,0,2)
46.37752
46.49328
46.42405
2.060311
44.99191
45.10766
45.03844
1.974451
After estimating the best-fit model, the next step
is to compare the efficiency of both models GARCH
and ARIMA fact that which model suits which
commodity, and this is done based on some
important statistics which are Hannan, Schwarz,
Akaike, and Durbin Watson. For this, we needed to
run the GARCH model on all three commodities. So,
after this next step is the estimation of the GARCH
model on these data sets. GARCH (1,1) model is
applied to conduct both the in-sample and out-of-
sample forecasting for Gold, Silver, and Crude oil
futures. After the application of the ARIMA and
GARCH models, a further step is to conduct the
comparison between both model sets based on the
above-mentioned facts. The next step is to predict the
best-fit model of ARIMA for each commodity.
Different models were generated to find out an
accurate one. The model is selected based on some
statics of the ARIMA model. The model with the
maximum R-square, Adjusted R-square, Likelihood
values, and Minimum Hannan, Schwarz, and Akaike
values and the Durbin Watson should be around two,
and the p-value less than 0.05 is selected for each
commodity. Detailed modeling was done to predict
the best-fit model for crude oil, gold, and silver
futures. The model is selected based on some statics
of the ARIMA model. The model with the maximum
R-square, Adjusted R-square, Likelihood values, and
Minimum Hannan, Schwarz, and Akaike values and
the Durbin Watson should be around two and the p-
value less than 0.05 is selected for each commodity.
Detailed modeling was done to predict the best-fit
model for crude oil, gold, and silver futures. The
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Shamsul Nahar Abdullah, Iqra Khan,
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following table represents the best-fit models of
ARIMA for all these commodities. The ARIMA
model is applied to the data of crude oil futures and
consists of 84 observations. The coefficients of
AR(1) are -0.449 and MA(3) is -0.334. Both statics
are identified as highly significant because their p
values are 0.000 and 0.0006 respectively, which are
lower than 0.05. Based on the results shown in Table
4, ARIMA is identified as the best-fit model for gold
futures because Akaike, Hannan, and Schwarz values
are less than the predicted values in the GARCH
model. And the value of Durbin Watson is closer to 2
as well and less than the value derived by GARCH.
By analyzing the estimated results of the ARIMA
model for gold, results depict that the p-value is
0.0257 which is less than 0.05 which concludes that
this model is an overall good fit for the study and for
efficiently analyzing the variables consisting of 84
observations. The coefficients of AR (4) are 0.1588
and MA(1) are 0.542. Both statistics are identified as
highly significant because their p values are 0.02 and
0.000 respectively, which are lower than 0.05. A
comparison of the ARIMA and GARCH models for
forecasting volatility in crude oil, gold, and silver
futures shows that both models can provide accurate
forecasts, but their performance may depend on the
specific market under consideration. While the
ARIMA model is suitable for modeling short-term
volatility, the GARCH model is more effective in
capturing the long-term persistence of volatility.
Moreover, the GARCH model can capture the
asymmetric response of volatility to shocks, which is
prevalent in futures markets.
5 Conclusion
The study tried to recommend a suitable model for
the prediction of the volatility of futures prices of
Crude oil, Gold, and silver from PMEX to provide
insights to the investors. For forecasting, GARCH
and ARIMA Models are used to conduct the
comparison among them and to recommend the best
model for the prediction of the futures of three key
commodities of PMEX. The results by taking the
daily data from 2010-2021 revealed a mixed
recommendation about the suitable model and
identified ARIMA as the most beneficial model for
the prediction of futures of crude oil and gold while
for the prediction of silver futures, GARCH(1,1) is
recommended as the most suitable model. Based on
the trend line, the results of this research also
revealed an asymmetrical effect on the volatility of
futures of crude oil and gold. However, for silver, the
trend line shows persistence over time. The study
recommends that gold and crude oil futures prices are
more volatile and unstable as compared to the silver
futures price in Pakistan. The time jump like political
or economic shift affects the volatility of the futures
price of these commodities positively or negatively
depending on the nature of the shocks. The results
are useful for the economic agents, managers, and
policymakers that have an interest in commodities
trading, and its volatility affects their potential to
invest. Thus, the international markets that trade in
such commodities may analyze the dynamics of
fluctuation in the commodity futures to build
efficient risk hedging models by implementing the
appropriate policies to suppress the financial stress in
the markets. The results will also help in analyzing
the intensity of the variation of commodities that will
provide them to diversify their investments with the
strategies and identify the information across the
commodity future markets. Future research may
include the macroeconomic effect of variables like
interest rate, international reserves, trade flows, and
openness on volatility in developing countries like
Pakistan. Similarly, researchers can consider the
spillover effect, leverage effect, and geopolitical risks
on oil prices and metals futures volatility. Different
methodologies can also be utilised to study the
leverage effect and to predict gold, silver, and crude
oil futures price volatility.
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