Comparative Analysis of the Performance of Expert Systems and
Machine Learning Models in the Context of the Islamic Stock Market
KAOUTAR ABBAHADDOU, MOHAMMED SALAH CHIADMI
Study and Research Laboratory in Applied Mathematics,
Mohammed V University in Rabat,
Mohammadia School of Engineering, Rabat,
MOROCCO
Abstract: - In this article, we will compare the performance of the autoregressive statistical methods of time
series ARIMA-GARCH (Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional
Heteroscedasticity) and the machine learning methods, mainly ANN (Artificial Neural Networks) and SVM
(Support Vector Machines). Different methods are suggested in the literature to enable the prediction of the
direction of stock market returns. However, with recent improvements in technology, statistical and
mathematical have been the most widely used. For this reason, our article focuses on their comparison to test
the diverging results in literature when it comes to comparing their performance. The empirical study will rely
on Islamic stock indexes as this area needs more research. Regarding the performance, it is evaluated based on
two criteria based on calculating the Mean Absolute Percentage Error and the Root Mean Square Error. Hence,
after the analysis of the results, we can confirm that neural networks are efficient compared to other methods.
Keywords: - Islamic finance, Stock price prediction, Machine Learning, Autoregression.
Received: August 28, 2021. Revised: June 12, 2022. Accepted: June 21, 2022. Published: July 11, 2022.
1 Introduction
In finance, predicting the future performance of an
index and knowing ahead of time the return on a
security, is a major concern, even with limited
precision. Hence, in reality, providing this kind of
information is not easy. Markets have more than
one dynamic behavior in practice. These
observations, empirically prove the utility of
considering complex, possibly non-linear models
capable of modeling different dynamics from a
single series. Thus, this kind of model should
consider a limited number of underlying dynamics
and model different phenomena causing behavior or
another. Moreover, these models should be
relatively simple to develop and adapted according
to the available data.
Most investors who wish to engage in the stock
market for the long term begin with fundamental
analysis to evaluate a company, a stock, or the
market as a whole. This form of study aims to
identify a financial asset's theoretical worth to
compare it to its current market value. Next, we
have technical analysis (TA) which differs from
fundamental analysis as it does not take into account
theoretical value or other basic elements.
This third way to evaluate the market is through
econometric models, which are probabilistic
mathematical models that attempt to characterize the
random relationships between the variables they
include. They've been used to try to explain why
time series of financial asset prices show positive
autocorrelations.
The fourth way is artificial intelligence, which is a
sort of knowledge gained by computers for them to
function and react in the same way that people do.
Machine learning is an area of artificial intelligence
concerned with the design and development of
algorithms that enable a computer (or a machine) to
learn to do extremely complicated tasks without
being explicitly programmed. This means that
machine learning approaches seek to uncover links
between data, extract knowledge from it, and apply
it to new data, rather than an algorithmic system
based on established rules that aim to duplicate or
entirely reproduce the decision-making process of
an expert.
In this paper, after going through the literature,
different non-linear prediction methods will be
presented and compared, namely autoregressive
statical methods ad machine learning models as
these are the most used and accurate methods in the
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current era. The basic idea is to take advantage of
the information available in the data from the past
evolution of the series and use it to determine, at
least partially, its future evolution. These methods
aim to show empirically, that a model covering
several dynamics can predict financial series and
affirm which one is the most productive.
2 Literature Review
The financial literature pays a lot of attention to the
question of market efficiency. On the one hand,
some defend the idea that financial asset prices vary
randomly and independently from previous
statements. Thus, they support the idea that
generating more profit comes mainly from taking
more risks. While, on the other hand, others argue
that financial series are predictable and are not
completely ruled by chance. In this sense, Louis
Bachelier (1900) indicates that the trajectory of
stock prices is only a succession of random steps
[1]. Hence, this implies that the mathematical
expectation of a speculator is zero. On the other
hand, Fama in the year 1965 carried out an
empirical study of market efficiency, where he
concluded that the prices of stock market assets
adjust instantly to the arrival of new information [2].
Next, Harry Roberts (1967) suggested dividing
efficiency into three forms (weak, semi-strong, and
strong) depending on the type of information that
the market takes into consideration to reflect the
current prices of securities [3]. However, Samuelson
in the year 2016 shows that prices fluctuate
randomly based on the concept of a martingale [4].
There are several approaches to analyzing and
predicting market developments. First, we can find
the sentiment analysis that considers non-
quantifiable data in its approach and analyzes the
public flow of information like articles and
publications to get an overall insight into the trend
of the stock market. On the other hand, we have the
fundamental analysis which is based on studying
microeconomic factors like debt levels and
macroeconomic factors such as inflation to explain
the change in prices in the medium to long term. In
this respect, Cheung, Chung, & Kim, 1997, Chung
& Kim, 2001 and Lo & MacKinlay, 2002 carried
out a series of statistical analyzes over the period
between 1988 and 2000 and concluded that the
prediction of the intrinsic value of stocks is possible
using models that rely on financial ratios and the
cost of equity [5, 6, 7]. Next, we have the technical
analysis that uses historical data of stock to help us
get an idea about trends of future movements. This
way, Lo, Mamaysky, & Wang, (2000) in their study
confirmed the power of the technical analysis to
predict the movements of financial assets by
analyzing the results of technical analysis on US
equity markets from 1962 to 1996 [8]. Also, Brock,
Lakonishok, & LeBaron in the year 1992 showed
that these rules were able to generate more profit
than the market by analyzing a 90-year history of
daily Dow Jones stock prices Besides, we have
quantitative methods that will be subject to
comparison in our article [9]. These methods use
mathematical modeling, econometrics, and
advanced computational techniques for the analysis
and forecasting of movements in financial series.
We can define an econometric model as a
probabilistic mathematical model that attempts to
describe the random relationships between the
variables included in these models. They have been
used in the finance market to try to explain the
positive autocorrelations of the time series of
financial asset prices.
Among the most used statistical methods, we have
the family of ARIMA (Autoregressive Integrated
Moving Average) approaches. The ARIMA model
was introduced in 1970 by Box and Jenkins. It
predicts the future values of a univariate time series
[10]. This model includes an autoregressive (AR)
part which describes the dependence between a
current moment and past moments and a moving
average (MA) part which captures the forecast error
at past moments. This methodology was very used
for short-term forecasting and quickly established
itself as an essential base for comparison. Many
extensions of this method have been suggested
subsequently. The ARIMAX method makes it
possible to integrate exogenous variables into the
model. It is used in particular to integrate
meteorological data into the forecast, but also
information from data provided by a clustering
algorithm. The Seasonal ARIMA (SA-RIMA)
model is used to model the seasonality of data. A lot
of studies fall into this scope, like the work of
Hamilton in 1994 and Lo and Mackinlay in 2002
which describes all the econometric models and
techniques used for the analysis and prediction of
financial time series [11, 7]. Moreover, Jarrett, J., &
Schilling, J. in 2008 concluded from their
experience in the German market that autoregressive
econometric models can predict the change in the
returns of the stocks used [12].
Therefore, the majority of studies have shown the
existence of positive autocorrelations for financial
time series, which means that autoregressive models
are useful for the prediction of these series. Today,
the financial markets have access to other
interesting measurement tools, rather than the
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statistical approaches that take into account the wide
range of available information. This approach is
artificial or machine learning, which is a field of
artificial intelligence that studies algorithms or
statistical models that allow a computer to perform a
specific task without a set of explicit instructions,
but by relying on the discovery of patterns and the
principle of inference. The algorithm is presented
with training data, from which it will learn a
mathematical model allowing it to make decisions
or make predictions without being explicitly
programmed to perform this task. Following this
learning phase, the learned model is used in a
production phase to complete the task from new
input data.
There are different types of machine learning,
depending on the type of data used or the type of
task being learned. Supervised learning algorithms
build a mathematical model from labeled data,
which contains the desired input and output of the
model. The model can therefore be trained to reduce
its error on the output examples. Unsupervised
learning algorithms learn from input data and
discover structure in that data, such as groups of
similar inputs (clustering). These algorithms are not
guided by labeled data describing the expected
output for a given input. Reinforcement learning
algorithms are concerned with the behavior of
software agents, which can perform actions in an
environment. The agent is rewarded (or punished)
for the result of his actions and the goal is to learn
how to maximize a notion of cumulative gain on his
actions. Here also, several researchers have studied
the effectiveness of these techniques. For example,
Neely & Weller in the year 2001 used genetic
programming to generate trading rules. These rules
have shown a very strong performance in the
exchange rate markets. Fernandez-Rodrıguez,
Gonzalez-Martel, & Sosvilla-Rivero in the year
2000 in turn used machine learning, choosing neural
networks as predictive models and technical
indicators as input data and they found that this
trading strategy outperforms the one of a passive
strategy for bearish and stable markets, but not
bullish ones [13].
Following this literature review, it is clear that we
have many approaches for market analysis and
prediction. Some attempts to reveal the most
performant approaches were held. Turban in 1996,
by using a sample of 58 companies, compared
Multiple Discriminant analysis (MDA) predictions
and artificial neural network (ANN) predictions and
found that ANN is better than MDA and can
improve the quality of communication. decision
making of an investor [14]. However, these results
do not allow us to say if ANN can make obtain
exceptional gains. Similarly, Beyaz, Tekiner, Zeng
& Keane (2018) compared the performance of
fundamental analysis, technical analysis, and the
combination of the two to predict the future price of
stocks, applied to machine learning models [15].
They put together historical data from 140 S&P 500
companies. They decided to use the RMSE to
measure the degree of error. Regardless of the
period considered, fundamental analysis
outperforms technical analysis because it offers a
smaller Root Mean Square Error (RMSE). However,
the combination of the two appears to reduce further
this measure of the level of error. If we compare the
performance of the two algorithms, regardless of the
period or which metrics were used, the support
vector regression (SVR) model offers the best
predictions.
Nevertheless, as we can see the results differ and
quantitative methods were rarely compared against
each other. That’s why we will focus this study on
comparing a statistical method ARIMA-GARCH
and two machine learning methods that showed
relevant results in price trend prediction from
previous studies, namely artificial neural networks
and support vector machines. The empirical study
will be done on Islamic stock indexes because this
market is often under-looked and present limited
literature that focuses mainly on studying the
performance of Islamic indexes like the one of Atta
in 2000 who used weekly data from the DJIMI
index from January 1996 until December 1999. The
study concluded that the Islamic stock index
outperforms its conventional counterpart. Ahmad
and Ibrahim (2002) studied the Malaysian market
from April 1999 to January 2002 [16]. In turn, they
compared the daily returns of KLSI, the Islamic
index of the Malaysian stock exchange, with its
conventional benchmark with a risk-free rate. The
results showed that Islamic indices fail to
outperform the market as well as the absence of a
significant difference in performance between
Islamic stock indices and the benchmarks used.
Hussein (2004) was interested in the English stock
market and analyzed the monthly values of the
Sharia index of the FTSE family from July 1996 to
March 2000 (upward period), then from April 2000
to August 2003 (downward period) [17]. The results
of his research corroborate those of Ahmad and
Ibrahim (2002) [18]. In two subsequent studies,
Hussein and Omran (2005) [19], as well as Girard
and Hassan (2005) [20], found similar results in
their study on DJIMI.
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3 Data and Methodology
3.1 Data Preparation
To compare the performance of the classical statical
model ARIMA-GARCH against two machine
learning model artificial neural networks and
support vector machines in the context of the
Islamic stock market, we will use two Islamic
indices:
- Morgan Stanley Capital International Islamic
(MSCII) was launched in 2007 and covers 69
countries.
- Jakarta Islamic Index (JKII) started in 2000 and is
composed of 30 companies specializing in the
production and distribution of food.
Our dataset is made of the historical daily data of
these two indices over 10 years and contains six
characteristics (Open, High, Low, Close, Volume,
and finally the Adj. Close).
In the context of studying data, the data typically
needs to be manipulated before a prediction model
can be used. We replaced data using different
methods like suppression or replacing them
depending on the nature of problems with the data,
namely missing data, outliers, or duplicated data.
Machine learning models need to depend upon
independent variables that we defined to be able to
make an accurate prediction. Three variables were
used for this matter. Mainly, the difference between
the opening and closing price, the difference
between the highest and lowest prices, and finally,
the difference between the traded volume over two
consecutive days.
A dependent variable should be defined as well in
all cases and it represents the value the algorithms
try to predict while relying on independent
variables. Thus, the chosen variable in our case
determines the price of the next day.
Separating the dataset is an essential step in building
a machine learning model. In our case, 80% of the
dataset will be used for training the model and 20%
will be used to test their performance. Since the
more data is afforded for training, the most robust
our model will be.
3.2 Statistical and Machine Learning
Models
In the context of this study, two machine learning
algorithms and one statistical model were
implemented. All algorithms were implemented in
R.
Support Vector Machines (SVMs):
Support Vector Machines are a set of supervised
learning techniques designed to solve ranking,
classification, and regression problems. SVMs are a
generalization of linear classifiers.
SVMs were developed in the 1990s from the
theoretical considerations of Vladimir Vapnik on the
development of a statistical theory of learning: the
Vapnik-Chervonenkis Theory. SVMs were quickly
adopted for their ability to work with large data, the
low number of hyperparameters, the fact that they
are well founded theoretically, and their good results
in practice [21].
The basic principle of SVM is to reduce the problem
of discrimination to a linear problem of finding an
optimal hyperplane. Two principles make it possible
to achieve this objective. The first consists of
defining the hyperplane as a solution to an
optimization problem under constraints whose
objective function is expressed only using scalar
products between vectors. Knowing that the number
of active constraints or support vectors controls the
complexity of the model. Secondly, the transition to
the search for nonlinear separating surfaces is
obtained by the introduction of a kernel function in
the scalar product implicitly inducing a nonlinear
transformation of the data using an intermediate
space that we can call feature space. Hence, the
commonly encountered name of the kernel machine.
On the theoretical level, the kernel function defines
a Hilbertian space, said to be self-reproducing and
isometric by the nonlinear transformation of the
initial space used to solve the linear problem.
We used the package ‘e1071’ for SVM in R to be
able to implement SVMs. After testing the radial,
linear and polynomial functions, the radial one was
chosen as it has better precision as well the value of
the cost was set to 128.
Artificial Neural Networks (ANN):
The origin of the development of neural network
technology lies in the desire to develop an artificial
system capable of performing intelligent tasks
similar to those performed by the human brain.
Neural networks are similar to the human brain
when you consider their two properties. First, a
neural network acquires knowledge through
learning. Secondly, the knowledge of a neural
network is stored in forces of inter-neuronal
connection known as synaptic weights.
The real advantage of neural networks lies in their
power, their ability to represent both linear and non-
linear relationships, and their ability to learn these
relationships directly from the modeled data series.
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These networks are composed of Inputs (synapses),
allowing them to receive external influences. Each
input is characterized by a specific weighting
coefficient (its synaptic weight W) which varies
over time, depending on the inputs presented. The
second component is a nucleus whose state is
determined by the value of the input weighted by W.
The last component is the output that reflects the
influence of the neurons on the outside, its value
depends on the state of the nucleus; it is linked to it
by a function (filter) which is generally nonlinear
and given by the following formula:
(1)
Where
,
With are Synaptic weights and the outputs of
the predecessors of the neuron.
In our algorithmic implementation, we used 5 layers
with 9 neurons on each layer, the activation function
was the sigmoid one and we used the ‘neuralnet’
package in R for that purpose.
Autoregressive Integrated Moving Average -
Generalized Autoregressive Conditional
Heteroscedasticity (ARIMA-GARCH) :
ARIMA is composed of two main parts AR and MA
which we are going to explain first.
An AR process stands for ‘autoregressive’.
Concretely if we consider a stationary process ,
this process is autoregressive of order p if we can
give its value at time t using its previous p terms.
Mathematically, it means that:
(2)
with the error and (, ..., ) are real numbers.
MA stands for ‘moving average’. If is a time
series, we consider that it is an MA process of order
q if we can express its value at time t as a linear
combination of random errors or what we call white
noises. Mathematically we translate this by:
(3)
with the error and (, ..., ) are real numbers.
If we combine these two processes, we obtain an
ARMA model. This makes it possible to model
more complex time series. An ARMA model of
order (p, q) is therefore written mathematically in
the form:
(4)
with the error, (, ..., ) and (, ..., ) are
real numbers.
However, one of the limitations of this model is that
it can only model stationary time series.
Thus, it cannot model a time series with an
increasing linear trend. To overcome this problem,
the ARIMA model was developed.
The I of the ARIMA model stands for 'integrated'
for integration. Thus, it becomes possible to remove
the trends in times series by calculating the
difference to make them stationary. If we take the
example of a time series with a linear trend of the
form:
(5)
(6)
So, by differentiating the series once, the linear time
dependence is eliminated and the difference is
stationary. Likewise, a quadratic trend can be
eliminated by differentiating the series twice. Once
the series is stationary, it is then possible to apply
the ARMA model.
The ARIMA model is therefore a combination of
this differentiation process and the classic ARMA
process.
The ARIMA (Autoregressive Integrated Moving
Average) processes were developed by BOX and
JENKINS (1976) is the generalization of ARMA
models for non-stationary, trend-admitting
processes (ARIMA) [10].
The ARCH stands for Auto-Regressive Conditional
Heteroskedacity and the GARCH stands for
Generalized ARCH. This is a type of model that
allows you to estimate and predict the volatility of a
stock's price or short-term return based on the values
that those prices or returns take a few periods
before.
The term Autoregressive means that we regress the
model from itself, that is to say, that the exogenous
variables are the lags of the endogenous variable at
order q. The term Heteroskedacity emphasizes the
fact that the variance is not constant over time. We
say that there is heteroskedasticity if there is in the
time series one or more sub-periods whose variance
is different from the variance of the other periods. In
financial series, the variation in variance is often
caused by a particular event that may arise in the
market. Thus, if the variance is heteroscedastic, it is
linked to market interactions.
The interesting thing in ARCH models is that it
takes into account not only the value of the
variable at different periods but also the change in
the value of the variance during these periods.
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Therefore, this contributes to greatly improving the
forecast of volatility.
The ARCH model was introduced by Engle in
1982 [22]. An ARCH process of order p models a
time series, if denoting the error is formed of a
stochastic part , representing a strong white noise
and a standard deviation depending on time :
(7)
(8)
Where , and ;
GARCH models follow the same principle as the
ARCH model but adds a second member to the
equation which is the moving average of order q.
GARCH models of order p and q are written in this
form:
(9)
Where , , , and ;
Finally, we can say that ARIMA-GARCH is a
combination of ARIMA et GARCH.
Mathematically, it is written as follows:
(10)
(11)
(12)
Where , , , , ,
and ;
The main package used among others in this
implementation is ‘rugarch’. We set the model to
GARCH(1,1). Regarding, ARIMA(p,q,d), d is set
to 0 and we implemented a function to search for
the best combination of p and q where these orders
can take values from 1 to 5.
3.3 Performance Evaluation
Our performance evaluation is based on measuring
prediction errors. Let the error on the prediction
at period t, we define as the difference between
the estimated value of the prediction and the real
value .
(13)
Let , , , ..., be the error observed over the n
periods considered. Then, the Mean Absolute
Percentage Error (MAPE) will be:
(14)
This criterion measures the importance of errors.
The best model using this criterion will be the one
giving the lowest value.
On the other hand, we have The Root Mean Square
Error (RMSE) that will be:
(15)
This criterion measures the deviation of error. The
best model is the one giving a value close to zero.
We used the libraries ‘Metrics’ and ‘MLmetrics’
under R, to calculate these errors.
4 Empirical Results
We calculated MAPE and RMSE indicators to
verify which model performs better.
Table 1. Calculation of MAPE
MSCII
JKII
ANN
0,13
0,25
SVM
0,27
0,37
ARIMA-GARCH
0,41
0,39
Table 2. Calculation of RMSE
MSCII
JKII
ANN
3,36
1,19
SVM
4,74
1,76
ARIMA-
GARCH
6,13
1,90
Given that the results obtained are quite similar
according to the used criteria used, we will focus
first our attention on the MAPE (mean absolute
percent error) which remains a widely accepted
indicator for measuring the explanatory power of
models. It shows how well the model fits the data in
terms of absolute fit and how near the observed data
points are to the model's predicted values. This
accuracy metric can be expressed as a percentage
and it is easier to understand than the other accuracy
measures. For example, we can see that MAPE is
0,25 on JKII when we used ANN. It means that the
forecast is improper by 25% percent on average. In
our case, overall, we found that all of ANN's
benchmarks were inferior to those of SVM and
ARIMA-GARCH in MSCII and JKII cases.
However, we should note that even if the model fits
the data well, we can observe some MAPE numbers
are very high because we have data values that are
close to zero. It is mainly related to the fact that the
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metric divides by the absolute error by the actual
data. Thus, we can say that values near 0 can
dramatically inflate the MAPE.
On the other hand, we have the RMSE (root means
square error), which can be considered as the
standard deviation of a variance that is unexplained.
It has the advantage to have the same unit as the
predicted variable, which is useful. Lower RMSE
values suggest a better match. Hence, we can say
that the root means square error (RMSE) is a good
indicator of how well the model predicts the
response. Since the model's primary goal is
prediction, this is the most significant fit criterion.
In our case, we can say that the indicators show that
most of the models perform well. We have mainly,
the results of ANN are the smallest followed by
SVM and finally ARIMA-GARCH for both indices.
We can confirm then that our neural networks can
follow the evolution of the index and detect outliers
better than the ARIMA-GARCH model and SVM
which comes into the second position. Thus, we can
say that globally, artificial intelligence models
perform better than statistical models in our study.
These results are coherent because the artificial
intelligence method can learn from the data series
itself. Models can find relationships and trends in
data that are often too complex to recognize just by
modeling through mathematical formulas.
No matter the rigor of the method used, what
interests the forecaster is to forecast the evolution of
the stock market index, which calls for debates
around the efficiency of the market.
In our case, it is difficult to forecast accurately by
conventional statistical quantitative methods
because these models predict hardly turning points
and their performance decreases on long-term
predictions. The artificial intelligence methods are
thus more relevant. It is mainly possible to forecast
the index from its historical values using ANN or
SVM but it is not very reliable over the long term.
Indeed, the existence of anomalies reinforces the
inefficiency of the stock market. They are linked to
the microeconomic behavior of various
stakeholders. These anomalies include irrationality,
heterogeneity of information, or seasonal variations.
5 Conclusion
In recent decades, we have witnessed the
spectacular development of quantitative methods
applied to management in general and finance in
particular. These methods can be defined as a set of
formalized techniques aimed at providing decision
support through the logical processing of a set of
quantitative information. In this sense, the main goal
of this study is to analyze how new mathematical
and computational approaches such as artificial
neural networks (ANN) or support vector machines
(SVM) can contribute to a better forecast of stock
market stock values compared to the methods
usually used in this domain like the one used in our
study ARIMA-GARCH. Starting from the
comparison of the three methods applied to the
analysis of time series on stock market values of
two Islamic indices JKII and MCSII indices, we had
significant results both on the predictive
performance of the model and on its detection
capabilities. We showed the outperformance of the
new approaches mainly the ANN for a better
forecast, obtained thanks to the great flexibility of
these methods.
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DOI: 10.37394/232015.2022.18.93
Kaoutar Abbahaddou,
Mohammed Salah Chiadmi
E-ISSN: 2224-3496
978
Volume 18, 2022
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WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT
DOI: 10.37394/232015.2022.18.93
Kaoutar Abbahaddou,
Mohammed Salah Chiadmi
E-ISSN: 2224-3496
979
Volume 18, 2022
