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Expert Systems With Applications 44 (2016) 320–331
Contents lists available at ScienceDirect
Expert Systems With Applications
journal homepage: www.elsevier.com/locate/eswa
Integrating metaheuristics and Artificial Neural Networks for improved
stock price prediction
Mustafa Göçkena,∗, Mehmet Özçalıcıb,AslıBorua,Ay¸se Tu˘
gba Dosdo˘
gruc
aAdana Science and Technology University, Industrial Engineering Department, Ye¸siloba Yerle ¸skesi, 01180, Adana, Turkey
bKilis 7 Aralık University, Business and Administration Department, Kilis, Turkey
cGaziantep University, Industrial Engineering Department, Gaziantep, Turkey
article info
Keywords:
Artificial Neural Network
Genetic Algorithm
Harmony Search Algorithm
Stock market price
abstract
Stock market price is one of the most important indicators of a country’s economic growth. That’s why de-
termining the exact movements of stock market price is considerably regarded. However, complex and un-
certain behaviors of stock market make exact determination impossible and hence strong forecasting models
are deeply desirable for investors’ financial decision making process. This study aims at evaluating the ef-
fectiveness of using technical indicators, such as simple moving average of close price, momentum close
price, etc. in Turkish stock market. To capture the relationship between the technical indicators and the stock
market for the period under investigation, hybrid Artificial Neural Network (ANN) models, which consist in
exploiting capabilities of Harmony Search (HS) and Genetic Algorithm (GA), are used for selecting the most
relevant technical indicators. In addition, this study simultaneously searches the most appropriate number
of hidden neurons in hidden layer and in this respect; proposed models mitigate well-known problem of
overfitting/underfitting of ANN. The comparison for each proposed model is done in four viewpoints: loss
functions, return from investment analysis, buy and hold analysis, and graphical analysis. According to the
statistical and financial performance of these models, HS based ANN model is found as a dominant model for
stock market forecasting.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
A stock market is a public market to trade the company’s stocks
and derivative at an approved stock price (Preethi & Santhi, 2012).
Stock market provides opportunities for brokers and companies
to make investments on neutral ground and is one of the primary
indicators of a economic condition of the country (Perwej & Perwej,
2012). However, stock market is characterized by nonlinearities,
discontinuities, and high-frequency multi-polynomial components
because it is interacted with many factors such as political events,
general economic conditions, and traders’ expectations (Hadavandi,
Shavandi, & Ghanbari, 2010). Also, the fast data processing of these
events with the help of improved technology and communication
systems has caused the stock prices to fluctuate very fast. Thus many
banks, financial institutions, large scale investors and stock brokers
have to buy and sell stocks within the shortest possible time and time
span of even a few hours between buying and selling is not unusual
∗Corresponding author. Tel.: +90322 455 0000–2226.
E-mail addresses: mgocken@adanabtu.edu.tr (M. Göçken), mozcalici@kilis.edu.tr
(M. Özçalıcı), aboru@adanabtu.edu.tr (A. Boru), dosdogru@gantep.edu.tr
(A.T. Dosdo˘
gru).
(Bonde & Khaled, 2012). Robust and agile stock market is also highly
desirable in the field of finance, engineering and mathematics due
to high return possibility. It is generally seen as a peak investment
outlet. For these purposes, many researchers have been investigated
the predictability of the stock market by using of fundamental anal-
ysis, technical analysis, time series prediction, and machine learning
methods (Prasanna & Ezhilmaran, 2013). Besides, most of the com-
panies have created new methods for evaluating financial data and
investment decisions (Sureshkumar & Elango, 2012). Among them,
ANN approach has been thought as the best forecasting method
with a high level of validity in the fields of stock market forecasting.
However, some critical points of ANN structure should be carefully
analyzed. The definition what constitutes an optimal set of ANN
input variables can be considered one of the main problems in ANN
structure because the choice of input variables directly affects the
forecasting accuracy. Secondly, number of neurons (or units, nodes)
in hidden layer is also so important for ANN. It is an adjustable part
in ANN but unfortunately, there is no unique method for fixing the
optimum number of neurons in hidden layer for a particular problem.
Therefore, researchers prefer generally to use trial and error method
for this purpose. In this paper, we proposed hybrid methodology for
determining input variable and the number of neurons in hidden
http://dx.doi.org/10.1016/j.eswa.2015.09.029
0957-4174/© 2015 Elsevier Ltd. All rights reserved.
M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331 321
layer. GA and HS are used as a tool for improving ANN’s forecasting
performance. In literature, GA is often used with ANN for the purpose
of training the network, feature subset selection, and architecture
optimization. However, HS is generally not used with ANN for these
purposes. Therefore, our study is created alternative solution meth-
ods for stock market forecasting with better solutions. The contribu-
tion is structured as follows. Section 2 describestherelatedworks.
Then, we start describing solution methodology in Section 3.Section
4deals with results and discussions. Finally, Section 5 is devoted to
conclusions.
2. Literature
The importance of Turkish stock market has increased substan-
tially with the establishment of the Istanbul Stock Exchange in 1986.
Since its establishment in 1986, the ISE has followed a fast pace
growth in terms of trading volume, market capitalization, number
of listed corporations and foreign investment (Adaoglu, 2000). Also,
ISE characterized with high volatility in the market and such volatil-
ity attracts many local and foreign investors as it provides high re-
turn possibility (Cinko & Avci, 2009). Hence, forecasting stock market
movement has been the objective of the vast research papers apply-
ing different techniques. Among them, ANN is featured as being data
driven and, hence, does not require assumptions concerning data.
With such a feature ANN is a suitable technique in handling nonlin-
ear, highly complex and dynamic data of stock markets (Karymshakov
& Abdykaparov, 2012). In the literature, ANN is clearly explained
by Egeli, Ozturan, and Badur (2003). The authors used six different
ANNs which includes multi-layer perceptron (MLP) and generalized
feed forward to predict ISE market index value. Authors used previ-
ous day’s index value, previous day’s TL/USD exchange rate, previous
day’s overnight interest rate and 5 dummy variables each represent-
ing the working days of the week as inputs. The results showed that
for each ANN model, the highest accuracies were obtained with 1 hid-
den layer and also ANN models give more accurate results than the
ones based on moving averages. Guresen, Kayakutlu, and Daim (2011)
compared ANN models including MLP, dynamic ANN, and the hybrid
neural networks. It is observed that classical ANN model MLP gives
more reliable results than the other models used in this comparison.
Kara, Boyacioglu, and Baykan (2011) revealed that ANN works bet-
ter than Support Vector Machine in predicting the direction of stock
price movement in the ISE. In the study, parameters of ANN models
such as number of neurons in the hidden layer were determined em-
pirically. Also, ten technical indicators were selected as feature sub-
sets by the review of domain experts and prior researches. ¸Senol and
Özturan (2008) statistically demonstrated that ANN outperforms Lo-
gistic Regression methodology. In the study, ANN was used to pre-
dict the stock price behavior in terms of its direction. The best results
were obtained for ANN model with three inputs, 11hidden neurons
in the single hidden layer and one output with three indicators, rel-
ative strength index of 14 days, stochastic indicator for 14 days, and
stochastic moving average. Yildiz, Yalama, and Coskun (2008) utilized
ANN for forecasting the direction of the ISE National-100 using the
highest and lowest prices paid during the day, the closing price, the
exchange rate (as the US dollar), and response rates as an input vari-
ables. The results of the previous studies show that accuracy of stock
market prediction is generally between 60% and 76%, and hence more
robust ANN model is needed to increase prediction accuracy in Turk-
ish stock market.
Having highly functional stock markets and exchanges is incred-
ibly valuable all over the world is a well-known fact. Therefore, so
many types of ANN models are developed to search out more efficient
forecasting model. Chiu and Chuang (2003) showed that ANN has
ability for predicting tendency of Taiwan stock market. Five different
ANN models were developed to decide the number of input neurons
and hidden neuron. Also, the classification technique and clustering
method were used under framework of ANN with quantitative and
qualitative factors. Similarly, Aldin, Dehnavi, and Entezari (2012) used
ANN for stock price index forecasting on the Taiwan Stock Exchange.
Closing price, the high and low price index were converted into tech-
nical indicators for predicting the position of stock price movements.
In the study, neuron numbers in the hidden layer was determined
empirically. Dastgir and Enghiad (2012) evaluated Iran Stock Market
by focusing on forecasting Tehran Stock Exchange Price Index which
is the most significant index of Iran Stock Market. In the study, two
hidden layers were used with many combinations of architecture.
The number of neurons in each hidden layer was changed from one
to sixteen. Results of the study revealed that ANN model with three
hidden neurons on the first hidden layer and four hidden neurons
on the second achieved the best performance in Iran Stock Market.
Ruxanda and Badea (2014) presented different configured ANNs and
compared them in terms of forecasting errors while making predic-
tions on Bucharest Stock Market Index. Input variables were set based
on a stepwise forward regression. Adebiyi, Adewumi, and Ayo (2014)
found that 10 inputs obtained from the New York Stock Exchange
including open price, low price, high price, close price, and volume
traded, 17 hidden neurons, and one output neuron give more accu-
rate results in ANN model. Laboissiere, Fernandes, and Lage (2015)
used ANN to predict the maximum and minimum day stock prices
of Brazilian power distribution companies. In the study, correlation
analysis was used to select input variable and different ANN archi-
tectures were tested empirically. The best results were found with
one hidden layer and only five hidden neurons. Zahedi and Rounaghi
(2015) applied ANN and principal component analysis to predict
stock price on Tehran Stock Exchange. The results of the study show
that ANN model has superiority over its rivals. Also, principal com-
ponent analysis method can accurately predict stock price on Tehran
Stock Exchange using 20 accounting variables.
In this paper we review studies in the ANN literature which have
been used for stock market forecasting, results revealed that a dif-
ferent combination of attribute sets was experimented with differ-
ent ANN model parameter values and each study provides satisfying
result in existing condition but ANN architecture is very important
which directly affects system performance essentially. Hence, most
previous studies were focused on the improvement of the ANN archi-
tecture. However, there are few studies on the input variable selec-
tion from predetermined data set and there is no clear methodology
available for variable selection and determining number of hidden
neurons in hidden layer. Therefore, the basic idea that lies behind the
proposed models is not only selecting the most relevant input vari-
ables that are to be used by ANN models but also setting the number
of neurons in hidden layer by manipulating ANN structure via meta-
heuristics. Thus, proposed models based on GA and HS are applied to
improve forecasting accuracy and stability of ANN.
3. Solution methodology
3.1. Technical indicators
This section describes input variable selection methodology. For
each case, 45 technical indicators are considered as input variables.
Technical indicators are effective tools to characterize the real market
situation. Using technical indicators can be more informative than us-
ing pure prices (Nikfarjam, Emadzadeh, & Muthaiyah, 2010) and it is
very practical way for stock analysts and fund managers to analyze
stock market. On the other hand, this technique may not be a good
alternative solution for common investors because too many tech-
nical indicators are available to be considered as prediction factors
and the most commonly used technical indicators are ordinarily not
understandable. Therefore, selection of the useful technical indica-
tors accurately is the key issue to make a profit for those stock mar-
ket investors (Wei & Cheng, 2012). However, no method is successful
322 M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331
enough to consistently beat the market. Every stock index or stock
has unique characteristics. That means, say feature A might play an
important role in predicting future prices of stock X while feature
B might be regarded as redundant for that stock. For that reason it
seems that it is not possible to say that “feature A is a good predictor
for every stock”. Different features must be used for prediction at-
tempt in different time periods and/or different stocks. In our study,
technical indicators are applied as the input variables of ANN to fore-
cast the stock market index. GA and HS are integrated with ANN not
only for optimizing the architecture of ANN but also for determining
the indicators that has the most significant effect on the forecasting
performance. The underlying logic for using GA and HS for variable
selection is to evaluate the usefulness of indicators and eliminate ir-
relevant ones to simplify the proposed model. It should be noted that
there is no limit for the number of indicators to be considered by GA
and HS. In Table 1, all of the technical indicators considered in this
study together with the final indicator selection results of GA and HS
algorithms are illustrated. Note that, shaded variables are selected by
none of the optimization methods.
3.2. Artificial Neural Network
ANN is a computational network which attempt to simulate, in a
gross manner, the networks of nerve cell (neurons) of the biological
(human or animal) central nervous system (Graupe, 2007). The infor-
mation processing and physical structure of the brain is partially em-
ulated with a web of neural connections (Li, 1994) which has great ca-
pacity in modeling nonlinear systems. Also, ANN is known with good
generalization capabilities and is substantially robust against noisy
or missing data (Versace, Bhatt, Hinds, & Shiffer, 2004). On the other
hand, it is difficult to design ANN model for a particular forecasting
problem. Modeling issues should be considered carefully. Determin-
ing the appropriate architecture such as number of the input vari-
ables, hidden layers and hidden neurons in each layer can be consid-
ered as a critical factor (Vaisla & Bhatt, 2010). For example, number of
hidden layers and neurons in each hidden layer is proportional to the
ability of the network to approximate more complicated functions.
However, this does not infer that complicated structures of networks
will always perform better (Perwej & Perwej, 2012). If the network
has too many hidden neurons, it will follow the noise in the data due
to over parameterization leading to poor generalization for untrained
data (Subasi & Erçelebi, 2005). On the other hand, network with too
few hidden neurons would be incapable of differentiating between
complex patterns leading to only a linear estimate of the actual trend
(Kuru ¸s, Kılıç, & Uçan, 2013). To eliminate these hesitations, three dif-
ferent forecasting models are proposed in this study and their perfor-
mances are compared. The parameters of each proposed model are
given in Table 2.
From Table 2, it is apparently seen that as their name imply, the
parameters of the first two proposed models are set by using HS and
GA, respectively. Note that the third model does not employ any opti-
mization method. Thus, third model directly uses all considered fea-
tures for training the ANN. It should be noted that 10 neurons in the
hidden layer are selected arbitrarily for the third model. The general
architecture of proposed models is demonstrated in Fig. 1.
In Fig. 1, p is the input pattern, b1is the vector of bias weights
on the hidden neurons, and W1is the weight matrix between 0th
(i.e. input) layer and 1st (i.e. hidden) layer. a1is the vector con-
taining the outputs from the hidden neurons, and n1is the vec-
tor containing net-inputs going into the hidden neurons. a2is the
column-vector coming from the second output layer, and n2is the
column-vector containing the net inputs going into the output layer.
W2is the synaptic weight matrix between the 1st (i.e. hidden)
layer and the 2nd (i.e. output) layer and b2is the column-vector
containing the bias inputs of the output neurons. Each row of W2
matrix contains the synaptic weights for the corresponding output
Tabl e 1
Initial feature pool and final result of selection status.
HS GA
Technical indicators Is selected? Is selected?
(0: No) (0: No)
(1: Yes) (1: Yes)
1 Today’s close−previous
close price
00
2 Previous close price 1 1
3 Previous highest price 1 1
4Previouslowestprice 1 1
5 Previous open price 0 0
6 5 day simple moving
average of close price
00
7 6 day simple moving
average of close price
01
8 10 day simple moving
average of close price
00
9 20 day simple moving
average of close price
00
10 5 day exponential moving
average of close price
00
11 6 day exponential moving
average of close price
10
12 10 day exponential moving
average of close price
11
13 20 day exponential moving
average of close price
11
14 5 day triangular moving
average of close price
11
15 6 day triangular moving
average of close price
01
16 10 day triangular moving
average of close price
11
17 20 day triangular moving
average of close price
11
18 Accumulation/distribution
oscillator
01
19 Close price moving average
convergence/divergence
01
20 9-period exponential
moving average of MACD
01
21 Acceleration opening price 0 1
22 Acceleration highest price 1 0
23 Acceleration lowest price 0 1
24 Acceleration close price 1 1
25 Momentum open price 1 1
26 Momentum highest price 1 1
27 Momentum lowest price 0 0
28 Momentum close price 0 1
29 Chaikin volatility 0 1
30 Fast stochastic %K00
31 Fast stochastic %D11
32 Slow stochastic %K00
33 Slow stochastic %D10
34 William’s %R00
35 Relative strength index 1 1
36 Bollinger middle band 1 1
37 Bollinger higher band 1 1
38 Bollinger lower band 1 0
39 Highest high 1 0
40 Lowest low 1 1
41 Median price 1 1
42 Price rate of change 1 0
43 Typical price 0 0
44 Weighted close 0 0
45 William’s
accumulation/distribution
00
neuron (Ahmed, Jafri, Ahmad, & Khan, 2007). Firstly, the neuron re-
ceives information from the environment and then this information
multiplied by the corresponding weights is added together and used
as a parameter within an activation (transfer) function (Haider &
Hanif, 2009). The transfer functions are used to prevent outputs from
reaching very large values that can ‘paralyze’ ANN structure (Duch
& Jankowski, 1999). For hidden layer, suitable transfer function is
M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331 323
Tabl e 2
Parameters of the models.
Parameters HS-ANN model GA-ANN model Regular ANN model
Size of the input layer Determined by HS =23 Determined by GA =26 45
Number of neurons in hidden layer Determined by HS =17 De te rm ined by GA =210
Transfer function in hidden layer Sigmoid tangent Sigmoid tangent Sigmoid tangent
Transfer function in output layer Pure-linear transfer function Pure-linear transfer function Pure-linear transfer function
Training function Levenberg–Marquardt training algorithm Levenberg–Marquardt training algorithm Levenberg–Marquardt training algorithm
Fig. 1. Architecture of the proposed neural network (Ahmed et al., 2007).
particularly needed to introduce non-linearity into the network be-
cause it gives the power to capture nonlinear relationship between
input and output (Ravichandran, Thirunavukarasu, Nallaswamy, &
Babu, 2005). In this part, tangent sigmoid transfer function is applied
in hidden layer. However, the use of sigmoid units at the outputs can
limit the range of possible outputs to the range attainable by the sig-
moid, and this would be undesirable in some cases (Bishop, 1995).
Hereby, a pure linear function is selected in output layer. The pure lin-
ear transfer function calculates the neuron’s output by simply return-
ing the value passed to it. After ANN model is constructed, training
of ANN is the next important step of the forecasting model. Training
of ANN is an iterative process like weights and bias of the network.
In this paper, proposed ANN-based forecasting models are trained
by Levenberg–Marquardt (LM) algorithm with optimum network pa-
rameters. LM is a trust region based method with hyper-spherical
trust region (Burney, Jilani, & Ardil, 2005) and is used as an intermedi-
ate optimization algorithm between the Gauss–Newton (GN) method
and gradient descent algorithm. Also, LM addresses the limitations of
each of those techniques (Kermani, Schiffman, & Nagle, 2005). When
the current solution is far from a local minimum, the algorithm be-
haves like a gradient descent method: slow, but guaranteed to con-
verge. When the current solution is close to a local minimum, it be-
comes GN method and exhibits fast convergence (Lourakis & Argyros,
2005). However, it is important to note that LM is very efficient when
training networks which have up to a few hundred weights (Hagan &
Menhaj, 1994).
3.3. GA-ANN forecasting model
When building an ANN, a number of parameters should be consid-
ered and unlimited ways are available to construct ANN. In the litera-
ture, particularly, input variable selection remains an important part
of ANN model development, due to the negative impact that poor se-
lection can have on the performance of ANNs during training and de-
ployment post-development (Ma ´
ndziuk & Jaruszewicz, 2011). In this
study, we used GA to overcome drawbacks of the input variable selec-
tion. GA is a general adaptive optimization search methodology based
on a direct analogy to Darwinian natural selection and genetics in bi-
ological systems (Huang & Wang, 2006). GA ensures the development
of new and better populations among different species during evo-
lution. Although most standard meta-heuristic algorithms used only
information from a single individual, GA uses information of a pop-
ulation of individuals (solutions) when they conduct their search for
better solutions (Pardalos,Pitsoulis,Mavridou,&Resende,1995). Ad-
ditionally, it is important to note that GA has proved its success in
search and optimization problems. Its ability to exploit the informa-
tion accumulated about an initially unknown search space in order
to bias subsequent searches into useful subspaces can be given as the
main reason for the success. This is the key feature, particularly in
large, complex, and poorly understood search spaces, where classical
search tools (enumerative, heuristic, etc.) are inappropriate, offering
a valid approach to problems requiring efficient and effective search
techniques (Martínez & Lozano, 2008).
Fig. 2 depicts a synthetic scheme of the GA based selection of in-
put variables. The advantage of the GA-ANN model lies in synergy
between the GA, which is used for the selection of the variables to be
used, and ANN, exploiting the selected variables. In the same manner,
GA is used to determine number of neurons in hidden layer because
inadequate neurons can restrict the relationship or too many neurons
can cause overtraining. Certainly, getting the correct balance between
numbers of neurons directly affect forecasting accuracy in models.
Basically, GA-ANN model is shown in Fig. 3 and can be summa-
rized as follows. It divides dataset as training and testing dataset. Fur-
thermore, training data set is also divided into the subsets to give the
ANN generalization ability. For this purpose we evaluated the can-
didate solutions on different subsets and obtained a mean of mean
squared error (MSE). The minimization of this error is performed by
GA. Calculating MSE continues until stopping criteria is satisfied. Also,
GA has several genetic operators that can be modified to improve the
performance of particular implementations, namely representation,
selection, crossover, and mutation. These procedures are given in the
next sections.
3.3.1. Chromosome representation
Chromosome representation is the first and the most important
operator obtained by encoding of a chromosome to represent a so-
lution. In literature, binary encoding is the most commonly used in
GA and gives many possible chromosomes even with small number
of alleles (Rajasekaran & Pai, 2003). Similarly, binary encoding is used
in this study and chromosome is considered to be composed of two
parts: (1) variable selection and (2) determination of the number of
hidden neurons (Fig. 4). If a variable is selected, gene is coded as 1,
otherwise 0. Similarly, if a node is selected, gene is coded as 1, oth-
erwise 0. Total length of the chromosome is determined as the sum
of the total number of variables considered and the total number of
neurons considered.
GA starts with a randomly generated initial population. Initial
population consists of a number of chromosomes that represent the
number of variables and the number of hidden neurons. After all fit-
ness values for the whole initial population are obtained, the chro-
mosomes evolve through successive iterations called generations. To
enhance diversity of the generation and to generate the population
of the next generation, GA operators such as selection, crossover and
mutation are activated.
3.3.2. Selection operator
Individuals, called parents, are selected based on a selection rule
to generate new, better solutions for next generations. In this study,
stochastic uniform selection which lays out a line is used. This
method chooses an individual according to its scaled fitness value.
324 M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331
Fig. 2. Flow-chart representing the GAs based variable selection system (Cateni, Colla, & Vannucci, 2011).
Fig. 3. GA-ANN iterative process for variable selection and determination of number of hidden layer neurons.
Fig. 4. Chromosome representation.
3.3.3. Crossover and mutation operators
In crossover operator, two chromosomes are randomly selected
and their chromosome strings are randomly cut to produce new
chromosomes. In this respect, a pair of parents is firstly randomly se-
lected from the mating pool. Secondly, a point, called crossover site,
along their common length is randomly selected, and the informa-
tion after the crossover site of the two parent strings are swapped,
thus creating two new children (Otman & Jaafar, 2011). An illustrative
crossover operator utilized in this study, is shown in Fig. 5.
Then, mutation operator is applied to provide a small amount
of random search. Without mutation, offspring chromosomes would
be limited to only the genes available within the initial population.
M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331 325
Fig. 5. Illustrative example of crossover operator.
Fig. 6. Illustrative example of mutation operator.
Tabl e 3
Parameters of the GA.
Elite count 2
Crossover fraction 0.8
# of generations 100
Population size 20
Mutation should be able to introduce new genetic material as well
as modify existing one (Fig. 6). With these new gene values, the GA
may be able to arrive at a better solution than was previously possible
(Kougias & Theodosiou, 2010).
After mutation operator, the candidate solutions obtained by GA
proceeds to the phase II (fitness function prediction). Best two indi-
viduals are saved for the next generations. This iterative process is
repeated over many generations. The run of GA terminates when the
termination criterion is satisfied. The best individual ever encoun-
tered during the run is typically designated as the result of the run.
The parameters of the GA are given in Table 3.
3.4. HS-ANN forecasting model
HS is based on the improvization process of musicians in a band.
In HS algorithm, multiple harmonics groups can be used in parallel.
Proper parallelism usually leads to better implantation with higher
efficiency (Geem, 2006). The good combination of parallelism with
elitism as well as a fine balance of intensification and diversification
is the key to the success of the HS algorithm, and in fact, to the suc-
cess of any meta-heuristic algorithms (Yang , 20 09). HS is simple in
concept, few in parameters, easy in implementation, imposes fewer
mathematical requirements. Therefore, HS has been successfully ap-
plied as an optimization method in many scientific and engineering
fields and was reported to be competitive alternative to many rivals
(Mahdavia, Fesanghary, & Damangir, 2007). In this paper, we pro-
posed HS-ANN model for determining the most relevant input vari-
ables and the number of neurons in hidden layer. The first step in HS-
ANN model is to divide dataset as training and testing dataset. Fur-
thermore, training data set is also divided into the subsets to give the
ANN generalization ability. For this purpose we evaluated the candi-
date solutions on 5 different subsets and obtained a mean of MSE. The
minimization of this error is performed by HS. Details of the proposed
HS-ANN model are shown in Fig. 7.
To apply HS, the problem should be formulated in the optimiza-
tion environment, having an objective function and constraints as
Eq. (1) (Mahdavia et al., 2007; Yadav, Kumar, Panda, & Chang, 2012):
Minimize (or Maximize)f(x)
Subject to xi∈Xii=1,2,3,....,N(1)
where f(x) is the objective function with xas the solution vector com-
posed of decision variable xi,andXiis the set of a possible range of
values for each decision variable xi(Lxi≤Xi≤Uxi), where Lxiand Uxi
are the lower and upper bounds for each decision variable, respec-
tively. In addition, the values of different parameters of the HS algo-
rithm also have to be specified. These parameters include harmony
memory size (HMS), harmony memory considering rate (HMCR),
pitch-adjusting rate (PAR).
3.4.1. Initialize the harmony memory (HM)
The initial HM consists of an HMS number of randomly gener-
ated solution vectors. Each component of the solution vector in HM is
initialized using the uniformly distributed random number between
the lower and upper bounds of the corresponding decision variable
[Lxi,Ux
i], where 1 ≤i≤N.Theith component of the jth solution
326 M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331
Fig. 7. Flow-chart representing the ANNs based variable selection system.
vector is given by Eq. (2)
xj
i=Lxi+(Uxi−Lxi).rand[0,1](2)
where j=1,2,3, …, HMS and rand[0, 1] is a uniformly distributed ran-
dom number between 0 and 1. Each row consists of a randomly gen-
erated solution vector, and the objective function value for the jth
solution vector is denoted by f(xj). The matrix formed is governed by
Eq. (3).
HM(j,1:N)=xj
HM(j,N+1)=fxj(3)
The HM with the size of HMS ×(N+1)can be represented by a
matrix, as
HM =⎛
⎜
⎝
x1
1x1
2x1
3··· x1
Nf(x1)
.
.
.....
.
.
xHMS
1xHMS
2xHMS
3··· xHMS
Nf(xHMS)
⎞
⎟
⎠
In this study, each row of the matrix of HM coincides with a so-
lution. First value of each row gives the number of hidden layer neu-
rons. The rest gives the information of whether the considered vari-
able is selected or not. The last value of the row gives the objective
function of the related row (see Fig. 8).
M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331 327
Fig. 8. Representation of the HM matrix.
Tabl e 4
Parameters of the HS.
HMS 100
bw 0.2
HMCR 0.95
PAR 0. 3
Max iteration 10,000
3.4.2. Improvise a new harmony from the HM
Then, new harmony is improvised which is the essence of the
HS algorithm. In improvization, the HS generates a new harmony
vector, x=x
1,x
2,.....x
N, using the following rules: memory con-
sideration, pitch adjustment, and random selection. The original HS
algorithm consists of three operations for considering the computa-
tional intelligence or randomness as Eq. (4):
x
i∈xi∈x1
i,x2
i,...,xHMS
i,(HMCR)
xi∈Xi,(1−HMCR)(4)
In this step, a random number is generated. If this value is less
than HMCR, value of 1 is chosen, else value of 0 is chosen. After the
memory consideration, each decision variable is evaluated to deter-
mine whether pitch adjustment is necessary or not. This evaluation
is carried out with PAR parameter which is the probability of pitch
adjusting and identified as Eq. (5):
x
i=xi±rand(0,1)×bw with probability PAR
xiwith probability (1−PAR)(5)
where bw is the range of Xi, rand(0,1) is random number between 0–
1.Ifthevaluesare1inbothofPARandHMCR,thevalueischosen
for the new harmony. Other values are selected as 0. In this step, the
value of x
iis chosen randomly. The value of x
iis in the range of Xiand
it has probability of HMCR. Details are given in Fig. 9.
3.4.3. Generation of new HM
After selecting the new values, the objective function value is cal-
culated for new harmony vector. If this value is better than the worst
harmony vector in the harmony matrix, it is then included in the ma-
trix, while the worst one is taken out of the matrix. Then, harmony
memory matrix is sorted in descending order by the objective func-
tion value. These are repeated until the termination criterion which is
the pre-selected maximum number of cycles is satisfied. Parameters
oftheHSaregivenintheTable 4.
4. Results and discussions
The main purpose of this study is to propose new hybrid stock
price forecasting models to get more accurate and reliable forecast-
ing. In the first section, variables are determined for ANN model. In
Tabl e 5
Descriptive statistics of testing and training dataset.
Train dataset Test dataset
Mean 50082.53 74373.31
Standard deviation 14858.80 4494.85
Length (Days) 4000 160
regular ANN model, we used all the variables considered. However,
in GA-ANN and HS-ANN models; we reduce the input variable set to
an optimal subset. Among 45 relevant input variables, GA-ANN se-
lected 26 variables as the optimal input variable subset while HS-
ANN selected 23 input variables as the optimal variable subset. Sim-
ilarly, the optimal number of neurons in hidden layer is specified.
It should be noted that for both GA-ANN and HS-ANN forecasting
model, the number of hidden layer is considered to be 1. In regu-
lar model, 10 neurons in hidden layer are predetermined arbitrarily.
However, both GA-ANN and HS-ANN models characterized their own
number of neurons in the hidden layer. While GA is selected only 2,
HS has 17 neurons in hidden layer.
To construct ANN model; suitable training and testing samples
should also be selected. The first issue here is to split the data into two
separate sets, the training and testing data sets. Although there is no
general solution to this problem, several factors such as the problem
characteristic, the data type, and the size of the available data should
be considered in making this decision. In this study, price informa-
tion of BIST100 index between 08/06/2005 and 27/05/2013 (4000 ob-
servations) used as training dataset, and 28/05/2013 and 20/09/2013
(160 observations) used as testing the performance of forecasting
models. Details of training and testing data set are given in Table 5.
Nine different loss functions namely mean absolute error (MAE),
root mean square error (RMSE), mean absolute relative error (MARE),
mean squared relative error (MSRE), root mean squared relative error
(RMSRE), mean absolute percent error (MAPE), mean squared per-
centage error (MSPE), and root mean squared percentage error (RM-
SPE) are used to evaluate the performance of training and testing
data sets. Resulting values of these loss functions are summarized
in Table 6. Actual prices and predicted prices are compared for each
forecasting models.
According to the results, HS-ANN model outperformed other fore-
casting models in terms of all statistical loss functions. It should
be noted that regular ANN model produced the highest forecasting
errors. In general loss function values are smaller at training per-
formance. However this performance is not representative because,
training set is used in the training of the model. In order to assess
the performance of forecasting models, we have to test it with a new
dataset. This performance is called as the testing performance and is
a true indicator of the forecasting performance. Note that, all of these
indicators have the smaller-the-better characteristic.
328 M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331
Fig. 9. New harmony improvization concept for the proposed HS-ANN forecasting model.
Tabl e 6
Training and testing statistics of models.
ei=pi−aip: predicted
price, a: actual price
Training HS-ANN Training GA-ANN Training regular ANN Testing HS-ANN Testing GA-ANN Testing regular ANN
MAE 1
n
n
i=1
|ei|944.7658 978.9924 429.3262 2597.321 2950.251 2951.554
MSE 1
n
n
i=1
e2
i2475056 2916503 362116,2 11236305 12202954 14516650
RMSE 1
n
n
i=1
e2
i1573.231 1707.777 601.7609 3352.06 3493.273 3810.072
MARE 1
n
n
i=1
|ei
ai|0.019524 0.018384 0.008916 0.033814 0.038628 0.038191
MSRE 1
n
n
i=1
|ei
ai|20.000772 0.000681 0.000155 0.00181 0.001995 0.002256
RMSRE 1
n
n
i=1
|ei
ai|20.027787 0.026087 0.012447 0.042541 0.044671 0.047493
MAPE 100
n
n
i=1
|ei
ai|1.95244 1.838397 0.891558 3.381416 3.862837 3.819056
MSPE 100
n
n
i=1
|ei
ai|27.720985 6.805103 1.549378 18.09704 19.95454 22.55602
RMSPE 100
n
n
i=1
|ei
ai|22.778666 2.608659 1.24474 4.254061 4.46705 4.749318
Regular ANN produced the smallest errors on training dataset.
However in testing performance it produces the highest errors in al-
most all indicators except for MARE which means that regular ANN
memorizes the training set and lost the generalization ability. This
situation is also known as overfitting issue. When the performance of
HS-ANN and GA-ANN models are examined, it becomes clear that in
training dataset except for the first three indicators, HS-ANN model
produced higher errors in comparison to GA-ANN model. However,
in testing period HS-ANN model outperformed GA-ANN model which
means it produced less error. This also means that HS-ANN has better
generalization ability than GA-ANN model. Among the statistical loss
functions MAPE has the most human friendly characteristic and gives
the error in percent. Note that, HS-ANN model produced 3.38% error
which is an acceptable error rate.
Fig. 10 depicts actual and forecasted prices as a time series. Ev-
ery figure consists of two parts. In the upper side predicted and
M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331 329
020 40 60 80 100 120 140 160
6
7
8
9x 10
4
Actual Prices and HS ANN Forecasting Results
HS Predic ted
Actual Price
020 40 60 80 100 120 140 160
-15000
-10000
-5000
0
5000
Predicted - Actual Values
HS Predicted - Actual
020 40 60 80 100 120 140 160
6
7
8
9x 10
4
Actual Prices and GA ANN Forecasting Results
GA Predict ed
Actual Price
020 40 60 80 100 120 140 160
-10000
-5000
0
5000
Predicted - Actual Values
GA Predic ted - Act ual
020 40 60 80 100 120 140 160
6
7
8
9x 10
4
Actual Prices and Single ANN Forecasting Results
Single ANN Predicted
Actual Price
020 40 60 80 100 120 140 160
-10000
-5000
0
5000
Predicted - Actual Values
Single ANN Predicted - Actual
Fig. 10. Actual versus predicted prices as time series.
actual prices are illustrated while in the lower side predicted minus
actual values are shown. Difference values are useful to get a general
vision of how well the forecasting model is. It should be noted that
in a perfect prediction difference graph the values should lie around
zero. Since deviations from zero indicate a deviation from a good pre-
diction it could be said that HS-ANN prediction performance is better
than that of others. In GA and regular ANN models difference lines
are far away from zero line.
Statistical performance measurements do not have much meaning
for practical investors. Financial performance of forecasting model
must also be examined to evaluate forecasting model. We can simu-
late buying and selling behaviors of a typical investor. An investor will
buy stocks from the market if he/she expects an increase in prices.
Similarly if an investor anticipates a decrease in prices then he/she
will try to sell his/her financial assets in order to prevent a poten-
tial loss. We simulated the above mentioned simple trading logic us-
ing the prediction results (or predicted values) of the proposed mod-
els. A trading algorithm is developed to trade-on-paper along test-
ing period. This algorithm returned the paper profits obtained from
transactions. We neglected the trading costs and taxes to simplify the
calculations.
Similarly, financial performances of the proposed models are
compared with a passive trading strategy. In buy and hold strat-
egy, an investor buys stocks from the beginning of trading period
price and sells all of its assets from end of trading period closing
price. The return in percent from this transaction is calculated as
follow (Eq. (6)):
r=Pt−n−Pt
Pt−n
(6)
Tabl e 7
A Comparison of the proposed models’ performances with a passive trading strategy.
HS-ANN model GA-ANN model Regular ANN model
Return from
investment
0.060406 0.011221 −0.20626
Buy and hold −0.13405 −0.13405 −0.13405
where Pt−nand Ptrepresents the first-day and last day closing price
of stock index in testing period.
The result of trading strategy yields a loss of 13.41%. HS-ANN
model yields a return of 6.04% profit while GA-ANN model returns
only 1.12% of profit during 160 trading sessions. By the way, regular
ANN yields a loss of 20.63% as can be seen from Table 7.
5. Conclusion
Over the years, researchers around the world have been studying
to forecast the stock market price as precisely as possible to reach
the best investment decisions. However, there is no consensus on the
effectiveness of forecasting models and hence, research on improv-
ing the effectiveness of forecasting models has been continued. This
paper has proposed a new hybrid model, based on a heuristic opti-
mization methodology (HS or GA) and ANN, to improve stock market
forecasting performance in terms of statistical and financial terms.
With development of the hybrid ANN models we show that struc-
turing ANN has become easy in implementation because our pro-
posed models have great capability in variable selection and deter-
mining the number of neurons in hidden layer. In order to select the
330 M. Göçken et al. /Expert Systems With Applications 44 (2016) 320–331
most relevant technical indicators, we firstly set predetermined 45
variables and at the end of the analysis 26 and 23 variable are speci-
fied as non-redundant by GA and HS models, respectively. That means
the complexity of the variable selection is reduced to almost its half.
In addition, determining the optimum number of neurons in hid-
den layer eliminates the overfitting or underfitting problems of ANN
models.
Based on the results, the average stock price forecasting perfor-
mance of the HS-ANN (MAPE =3.38) is significantly better than
that of GA-ANN (MAPE =3.86) model and the regular ANN model
(MAPE =3.81). It should be noted that MAPE values with pro-
posed models are about 10% lower than the ones reported in existing
studies. Furthermore, MAPE results with the proposed models look
promising in emerging markets. Also, trading performances are quite
impressive in proposed models. HS-ANN (%6.04) and GA-ANN (%1.12)
models yield higher returns in comparison with regular ANN model
(−%20.63). Even operating in a bear market (buy and hold return is
−%13.41), forecasting models accomplished to yield a positive return.
Although proposed hybrid models of predicting stock market
prices using the GA and HS give remarkable results, this study has
some limitations. First, number of hidden layer is fixed at 1. Al-
though training becomes excessively time-consuming with increas-
ing number of hidden layers, the performance of the model can
change with the number of hidden layer. The second limitation is pre-
determined transfer and training functions because combinations of
training function and transfer functions may affect quality of ANN
models.
HS-ANN and GA-ANN can be used successfully to forecast the
stock market price movement in different stock markets. The other
good direction for future research would be to consider other pa-
rameters which may affect the ANN architecture such as number of
hidden layer, type of transfer function. Variants of the HS such as
improved HS, global-best HS are possibly used to increase in the ac-
curacy of the forecasting. Similarly, the effects of various GA including
many different forms of selection, crossover, and mutation operators
can be examined as a part of the approach used in this study.
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