A hybrid model based on rough sets theory and genetic algorithms for stock price forecasting

<sup>Ching-Hsue Cheng
a
, Tai-Liang Chen
b
, Liang-Ying Wei
c,
*
a
Department of Information Management, National Yunlin University of Science and Technology, 123, Section 3, University Road, Touliu, Yunlin 640, Taiwan
b
Department of Information Management and Communication, Wenzao Ursuline College of Languages, 900 Mintsu, 1st Road, Kaohsiung 807, Taiwan
c
Department of Information Management, Yuanpei University, 306 Yuanpei Street, Hsin Chu 30015, Taiwan
article info
Article history:
Received 26 November 2010
Received in revised form 21 December 2010
Accepted 8 January 2010
Keywords:
Rough set theory
Genetic algorithms
Cumulative probability distribution
approach
Minimize entropy principle approach
Technical indicators
abstract
In the stock market, technical analysis is a useful method for predicting stock prices.
Although, professional stock analysts and fund managers usually make subjective judgments, based on objective technical indicators, it is difficult for non-professionals to apply
this forecasting technique because there are too many complex technical indicators to be
considered. Moreover, two drawbacks have been found in many of the past forecasting
models: (1) statistical assumptions about variables are required for time series models,
such as the autoregressive moving average model (ARMA) and the autoregressive conditional heteroscedasticity (ARCH), to produce forecasting models of mathematical equations, and these are not easily understood by stock investors; and (2) the rules mined
from some artificial intelligence (AI) algorithms, such as neural networks (NN), are not easily realized.
In order to overcome these drawbacks, this paper proposes a hybrid forecasting model,
using multi-technical indicators to predict stock price trends. Further, it includes four
proposed procedures in the hybrid model to provide efficient rules for forecasting, which
are evolved from the extracted rules with high support value, by using the toolset based
on rough sets theory (RST): (1) select the essential technical indicators, which are highly
related to the future stock price, from the popular indicators based on a correlation
matrix; (2) use the cumulative probability distribution approach (CDPA) and minimize
the entropy principle approach (MEPA) to partition technical indicator value and daily
price fluctuation into linguistic values, based on the characteristics of the data distribution; (3) employ a RST algorithm to extract linguistic rules from the linguistic technical
indicator dataset; and (4) utilize genetic algorithms (GAs) to refine the extracted rules to
get better forecasting accuracy and stock return. The effectiveness of the proposed
model is verified with two types of performance evaluations, accuracy and stock return,
and by using a six-year period of the TAIEX (Taiwan Stock Exchange Capitalization
Weighted Stock Index) as the experiment dataset. The experimental results show that
the proposed model is superior to the two listed forecasting models (RST and GAs) in
terms of accuracy, and the stock return evaluations have revealed that the profits produced by the proposed model are higher than the three listed models (Buy-and-Hold,
RST and GAs).
2010-Elsevier Inc. All rights reserved.
0020-0255/$ - see front matter2010-Elsevier Inc. All rights reserved.
doi:
*Corresponding author.
E-mail addresses:[e-mail](C.-H. Cheng),[e-mail](T.-L. Chen),[e-mail] (L.-Y. Wei).
Contents lists available atScienceDirect
Information Sciences
journal homepage: www.elsevier.com/locate/ins
1. Introduction
In the stock market, it is very difficult to forecast stock trends because of complex factors influencing stock markets and
nonlinear relationships, which are contained among different periods of stock prices. Although only a few investors profit
from the stock market, millions of them still have not given up trying to make money from the market. Therefore, since
the first stock market opened, numerous forecasting methods have been employed in an attempt to predict stock prices.
In the area of stock market forecasting, the technical analysis method is one of the primary analytic approaches used by
investors to make investment decisions, and many researchers have been focusing on technical analysis to increase their
investment returns[4,13,15]. Furthermore, the technical analysis method has the ability to forecast the future price direction
by studying past market data, primarily stock price and volume. The technical analysis method assumes that stock price and
volume are the two most relevant factors in determining the future direction and behavior of a particular stock or market,
and that the technical indicators, coming from a mathematical formula, based on stock price and volume, can be applied to
predict price fluctuations and also provide data for investors, enabling them to determine the timing for the buying or selling
of stock[13].
Besides the technical analysis methods, many conventional numeric forecasting models have been proposed by financial
researchers, such as Engle’s[17] autoregressive conditional heteroscedasticity (ARCH) model, Bollerslev’s[6] generalized
ARCH (GARCH) model, Box and Jenkins’[7]autoregressive moving average (ARMA) model, and the autoregressive integrated
moving average model (ARIMA).
In recent decades, many researchers have employed another approach to financial forecasting: artificial intelligence
algorithms In 1990, Kinoto et al.[29] developed a prediction system for the stock market by using a neural network.
Nikolopoulos and Fellrath[32]combined genetic algorithms (GAs) and a neural network to develop a hybrid expert system
for investment decisions. Kim and Han[27]proposed a genetic algorithms approach in order to feature discretization and the
determination of connection weights for artificial neural networks (ANNs) to predict the stock price index. Huarng and Yu
[25] applied a backpropagation neural network to establish fuzzy relationships in fuzzy time series for forecasting stock
prices. Roh[42]integrated a neural network and time series model for forecasting the volatility of the stock price index.
From the literature noted above, however, three major drawbacks can be found in their forecasting methods and models:
(1) stock market analysts and fund managers apply various technical indicators to forecast stock market trends, based on
their personal experience, which could result in erroneous judgments of market signals; (2) for most statistical methods,
there are some assumptions about the variables used in the analysis, which can not be applied to those datasets that do
not follow the statistical distributions; and (3) the artificial neural network (ANN) is a black-box method, and the rules
mined from it are not easily understandable.
To improve upon past forecasting models, a revised model should be able to overcome the drawbacks contained in previous models and should offer a good methodology which could be used more easily by investors. Therefore, this paper proposes a hybrid forecasting model to refine past models in stock price forecasting, and provides four novel methods in the
forecasting processes: (1) select essential technical indicators by using a correlation matrix; (2) use CPDA (cumulative probability distribution approach) and MEPA (minimize entropy principle approach) to discretize condition features (technical
indicators) and decision features (daily price fluctuation); (3) apply the rough set theory (RST) to produce rules from the linguistic values of technical indicators; and (4) employ genetic algorithms (GAs) to refine the extracted rules to improve forecasting accuracy and stock return.
Empirically, this paper employs two types of stock databases (stock index and individual stock price) as experimental
datasets. From the model verification, it is shown that the refined processes are effective in improving forecasting accuracy,
and, based on the evidence, a stock analyst or investor can employ the refined processes proposed in this paper to improve
their forecasting tools or models.
The rest of this paper is organized, as follows: Section2introduces the related works; Section 3demonstrates the
proposed model and algorithm; Section4evaluates the performance of the proposed model and describes the findings;
and Section5draws conclusions and proposes recommendations for future research.
2. Related works
This section reviews related works of technical analysis, cumulative probability distribution approach, minimize entropy
principle approach, rough set theory, and genetic algorithms.
2.1. Technical analysis
Technical analysis is an attempt to predict future stock price movements by analyzing a past sequence of stock prices
[39]. It relies on charts and looks for particular configurations that are supposed to have predictive value. Analysts focus
on investor psychology, which represents common investors’ responses to certain price formations and price movements,
to analyze the fluctuations of stock market. The price at which investors are willing to buy or sell depends on personal expectation. If investors expect the security price to rise, they will buy it; if investors expect the security price to fall, they will sell
it. These simple statements are the cause for a major challenge in setting security prices, because they refer to human expec-1611
tations and attitudes[39]. It is said that, securities never sell for what they are worth, but for what people think they are
worth. It is very important to understand that market participants anticipate future development and take timely action,
which compels the price movement. Since stock market processes are highly nonlinear, many researchers have been focusing on technical analysis to improve investment returns [2,4,49].
2.2. Cumulative probability distribution approach (CDPA)
Probability refers to the study of randomness and uncertainty. In any situation, one of a number of possible outcomes may
occur. The theory of probability provides methods for quantifying the chances, or likelihoods, associated with the various
outcomes. Because a probability distribution on the real line is determined by the probability of being in a half-open interval
p(a, b], therefore,F(b)F(a)ifa<b. The probability distribution of a real-valued random variable Xis completely characterized by its cumulative distribution function (CDF)[1]. For every real number x, the CDF of Xis given by

where the right-hand side represents the probability (p) that the random variableXtakes on a value less than, or equal to,x.
CapitalFis used to represent the cumulative distribution function, in contrast to the lower-case f , used to represent
probability density functions and probability mass functions. The CDF ofXcan be defined in terms of the probability density
functionf , as follows:

Zx
1
fðtÞdt ð2Þ
The inverse of the normal CDF is computed with parameterslandrat the corresponding probabilities inP, where l
denotes the mean andrdenotes the standard deviation of the data[1]. The normal inverse function in terms of the normal
CDF is defined as
x¼F
1
ðpjl;rÞ¼fx: Fðxjl;rÞ¼pg; ð3Þ
where
p¼Fðxjl;rÞ¼
1
r
ffiffiffiffiffiffiffi
2p
p
Zx
1e
ðtlÞ
2
2r2
dt ð4Þ
The cumulative probability of normal distribution is used to determine the intervals. The steps of the cumulative probability distribution approach are as follows[14]:
Step 1: Test normal distribution.
In this approach, the data must be of normal distribution. This study utilizes CPDA because stock market fluctuations and
returns tend to be of normal distribution[3,47].
Step 2: Define the universe of discourseU.
LetU¼½D
r
min;D
þr
max, where DminandDmaxdenote the minimum and maximum values in historical data, andrdenotes the
standard deviation of the yearly data.
Step 3: Determine the length of intervals and build a membership function.
PLB, as the lower boundary of cumulative probability, and PUB, as the upper boundary of cumulative probability of each
linguistic value, are computed by
PLB ¼ð2i3Þ=2n ð25i5nÞ ð5Þ
PUB¼i=n ð15i5nÞ ð6Þ
whereidenotes the order of the linguistic values, andndenotes the number of linguistic values. The lower boundary of the
first linguistic value and the upper boundary of the last linguistic value correspond to the lower and upper boundary, respectively. This step computes the inverse of the normal CDF by Eqs.(3) and (4).
Step 4: Fuzzify the historical data.
According to the inverse of normal CDF, the lower boundary, midpoint and upper boundary as the triangular fuzzy number of each linguistic value, can be computed. The triangular fuzzy number is applied to build a membership function. The
membership degree of each instance is calculated to determine its linguistic value.
2.3. Minimize entropy principle approach (MEPA)
The purpose of entropy minimization analysis is to determine the information content in a given dataset. The entropy of a
probability distribution is a measure of the uncertainty of the distribution[51]. To divide the data into membership functions, establishing the point of segmentation between classes of data is needed. A point of segmentation can be determined
with an entropy minimization screening method; then, start the segmentation process by first dividing it into two classes.
Thereupon, a repeated partitioning with the value of segment point calculations will allow us to partition the dataset into a
number of fuzzy sets[43]. In recent years, MEPA has been used in forecasting problems [10].
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Assume that the value of the segment point is being sought for a sample in the range betweenx1andx2. An entropy equation is written for the regions½x1;xand½x;x2, and denotes the first regionpand the second regionq. Entropy with each value
ofxis expressed as: [14]
SðxÞ¼pðxÞSpðxÞþqðxÞSqðxÞ ð7Þ
where
SpðxÞ¼½p1
ðxÞlnp1
ðxÞþp2
ðxÞlnp2
ðxÞ
SqðxÞ¼½q1
ðxÞlnq1
ðxÞþq2
ðxÞlnq2
ðxÞ
ð8Þ
and wherepk
ðxÞandqk
ðxÞare the conditional probabilities that the classksample is in region½x1;x1þx and½x1þx;x2,
respectively, andpðxÞandq(x) are the probabilities that all samples are in region½x1;x1þx and½x1þx;x2, respectively.
pðxÞþqðxÞ¼1 ð9Þ
The value ofxthat gives the minimum entropy is the optimum value of the segment point. The entropy estimates ofpk(x)
andqk(x), andp(x) andq(x) are calculated, as follows:[14]
pkðxÞ¼
nkðxÞþ1
nðxÞþ1
ð10Þ
qkðxÞ¼
NkðxÞþ1
NðxÞþ1
ð11Þ
pðxÞ¼
nðxÞ
n
ð12Þ
qðxÞ¼1pðxÞ ð13Þ
wherenk(x) is the number of class k samples located in½x1;x1þx, n(x) is the total number of samples located in½x1;x1þx,
Nk(x) is the number of class k samples located in½x1þx;x2, N(x) is the total number of samples located in½x1þx;x2, and n
is the total number of samples in [x1,x2].
2.4. Rough set theory
Rough sets theory (RST) was proposed by Pawlak[33–37]in 1982. In recent years, RST has been used in economic and
financial prediction. Many researchers have applied RST to discover trading rules[20,48]. The concept of RST is founded
on the assumption that with every associated object of the universe of discourse, some information objects characterized
by the same information are indiscernible in the view of the available information about them. Any set of all indiscernible
objects is called an elementary set and forms a basic granule of knowledge about the universe. Any union of elementary sets
is referred to as a precise set; otherwise the set is rough.
With any rough sets, a pair of precise sets, called thelower and upper approximation, BX¼fxj½x
B#Xg and
BX¼fxj½x
B\X–;gof the rough sets, is associated[33]. The lower approximation consists of all objects that definitely belong to the set, and the upper approximation contains all objects that possibly belong to the set. The difference between the
upper and the lower approximation constitutes theboundary region, BNBðxÞ¼BXBX, of the rough sets. The set Xis called
‘‘rough” (or ‘‘roughly definable”) with respect to the knowledge in B, if the boundary region is non-empty. The basic notions
in rough sets are shown in Fig. 1.
The RST is a series of logical reasoning procedures used for analyzing an information system. An information system can
be seen as a decision table, denoted byS¼ðU;A;C;DÞ, where Uis the universe of discourse,Ais a set of primitive features,
andC;DAare two subsets of features, assuming thatA¼C[DandC\D¼;, where Cis called the condition attribute and
Dis the decision attribute. The measure to describe the inexactness of approximation classifications is called the quality of
Fig. 1.Basic notions of rough sets.
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approximation ofXbyB. It expresses the percentage of objects that can be correctly classified into class X,employing the
attributeB[33]:
c
B
ðAÞ¼
P
cardðBXiÞ
cardðUÞ
ð14Þ
If c
B
ðAÞ¼1 , then the decision table is consistent; otherwise, it is inconsistent.
An important issue in RST is attribute reduction in which the reduced set of attributes provides the same quality of
approximation as the original set. There are two fundamental concepts in connection with this attribute reduction. TheBreduct ofA, denoted by RED(B), is the minimal subset ofA, which provides the same quality of approximation of objects into
elementary classes ofBas the whole attributes ofA. TheB-core ofA, CORE(B), is the essential part ofA, which cannot be eliminated without disturbing the ability to classify objects into the elementary classes of B[33]. It is the intersection of all
reducts.
COREðBÞ¼
\
Ri2REDðBÞ
; i¼1;2;... ð15Þ
Using a reduced algorithm, the rules can be found through determining the decision attributes value, based on the condition attributes values. Therefore, the rules are presented in an ‘‘IF condition(s) THEN decision(s)” format. The concept of the
decision table is employed in this study to establish rules from fuzzy relationships, which generate rules for better forecasting results.
2.5. Genetic algorithms
Genetic algorithms (GAs) were advanced by Holland[24]in 1975, and expanded by Goldberg[21]in 1989. GAs are search
algorithms, inspired by evolution and applied in searching for the global optimum for many applications. Furthermore, GAs
have been successfully applied in economic and financial prediction[2,28]. These algorithms encode a potential solution for
a specific problem into a simple chromosome-like data structure and apply recombination operators to these structures to
preserve critical information. The steps of GAs in the proposed model, based on Goldberg[21], are reorganized for this study,
as follows:
Step 1:Initialization.
This step generates the initial population containingNP chromosomes, which are used to find global optimum initial
seeds, whereNPis the number of individuals in each generation. Simultaneously, the probability of crossoverPC, probability
of mutationPM, and the maximum numbers of generations NGare also initialized.
Step 2:Evaluation.
After the initialization step, each chromosome is evaluated using a user-defined fitness function. The fitness value of each
string is an index of the problem’s design improvement suitability and the probability of survival of reproduction in genetic
algorithms.
Step 3:Check termination criteria.
After the previous steps, the processes, from step 2 to 7, are repeated until the termination criteria are satisfied. The proposed algorithm is terminated if either one of the following conditions is satisfied:
1. The maximum number of generations is achieved, or
2. The same solution has not been changed for the present generation.
Step 4:Elitism mechanism.
In order to ensure the propagation of the elite chromosome, GAs use theElitism mechanism[44,50]. This mechanism selectsP% individuals, which have the best fitness values, to be the offspring of the next generation, while the remaining individuals execute the genetic operations (i.e., selection, crossover and mutation).
Step 5:Selection.
Selection is a process in which suitable chromosomes from the parents’ populations for the next generation are chosen. In
this step, the selection of this model istournament selection[5,22]. It is both effective and computationally efficient. Pairs of
chromosomes are selected at random to produce their own fitness values. The chromosomes with the best fitness values will
be chosen. This step is repeated until the number of chromosomes selected is equal to the number of the population.
Step 6:Crossover.
The crossover operates by swapping corresponding segments of a string representation of the parents and extends the
search for a new solution. Such positional bias[18]implies that the schemas with long-defining lengths suffer biased disruption. In order to reduce positional bias, this model usesuniform crossover[45], which can be disruptive especially to
the early generations. Uniform crossover operates as shown inFig. 2.
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Step 7:Mutation.
The mutation is a GA mechanism. It randomly chooses a member of the population and changes one randomly chosen bit
in its bit string representation. The mutation operation is shown in Fig. 3.
3. Proposed concepts and model
3.1. Proposed concepts
As stated in the previous section, past forecasting models exhibited three major drawbacks when used to predict stock
market activity: (1) utility technical indicators used to forecast stock prices represent a subjective approach because investors attempt to make knowledgeable judgments about future price trends, based on the values of the technical indicators; (2)
some prerequisites, such as statistical probability distribution[9], form the theoretical basis for constructing conventional
forecasting models, but usually stock data do not follow a specific data distribution; and (3) rule presentations of stock data,
produced from some data-mining algorithms, are difficult for non-professional investors to interpret[46] (i.e., the rules
mined from ANN are not easily understandable). We argue that these drawbacks reduce the efficiency and applicability
of the forecasting model, and to overcome these drawbacks, four novel methods are proposed in the processes of data-mining for stock price forecasting.
In the preprocess of data-mining, two objective approaches, CPDA (cumulative probability distribution approach) and
MEPA (minimize entropy principle approach), are suggested to discretize each technical indicator (condition features) and
daily price fluctuation (decision features) into linguistic values. There are advantages in using data discretization methods
in preprocessing raw data. For example, the data dimension of a database can be reduced and simplified, and use of discrete
features is usually more compact and shorter than the use of continuous ones [31]. Additionally, to reduce the amount of
stock data and find the effective indicators related to the future stock price, a ‘‘correlation matrix” can be used to select,
objectively, essential technical indicators from popular indicators, used in the stock market in the preprocess.
In the model-building process, a rough set (RS) algorithm is one proper data-mining algorithm suggested to extract forecasting rules from complex stock data. In recent data-mining techniques, RS methods have provided a basis for a predictive
data-mining tool that is especially helpful in dealing with vague, incomplete and uncertain data used for decision-making.
Three advantages can be discovered when applying RS methods: (1) RS theory can deal with the original datasets without
any additional information or statistical assumptions, unlike the probability of statistics; (2) RS theory can discover important facts hidden in datasets and express them with decision rules of natural language; and (3) the results (rules) from a RS
model are easily understood[16,23]. Because of these advantages, RS theory has become an important theory in the fields of
artificial intelligence (AI), knowledge discovery in database (KDD), and data-mining (DM). Accordingly, a forecasting model
using a RS algorithm to produce rules can overcome the limitations
1
of statistical methods for stock price forecasting, and the
produced ‘‘if-then” rules can model the qualitative aspects of human knowledge applicable for investors.
Moreover, genetic algorithms (GAs)[2,28]are an effective and robust method for searching for proper solutions to the
problems of very large spaces or dimensions in a variety of applications, and are particularly applicable in solving multiparameter optimization problems. In the stock market, ‘‘unexpected events,” which will turbulently influence stock price,
will sometimes occur. Although RS methods can extract rules effectively from past stock data, the rules to express the ‘‘unexpected events” have very low support value, and they are usually ignored when forecasting the future. Also, the ‘‘unexpected
events” in the future may not be similar to those of the past. Therefore, to meet the ‘‘unexpected events,” we use GAs to produce ‘‘mutation rules,” which are evolved from rules extracted from RS methods, to improve classification accuracy and forecasting profit. Consequently, to deal with the unpredictable variations contained in stock markets, GAs are suggested to
refine the extracted rules to enhance forecasting performance. The program of the proposed model can be downloaded
on the web page[52].
Before After
011
* * *
Parent 1 11011
Parent 2 0  0  1  0 1 1001
0 1 Offspring 1
1 Offspring 2
Fig. 2.The crossover operation for the proposed model.
Before After
1 1 0 1 1 11001
Fig. 3.The mutation operation.
1
Some statistical distributions are presumed as a basis to construct mathematical models, but usually stock data do not follow a specific data distribution.
1615
3.2. Proposed model
Based on the proposed concepts above, this paper suggests a hybrid model (the overall framework of which is shown as
Fig. 4), which incorporates four novel data-mining methods (including CPDA, MEPA, RST and GAs) in the forecasting processes, and provides three major phases (including six processes), as noted below.
3.2.1. Preprocess
There are two works contained in this phase, as follows:
3.2.1.1. Data transformation and selection of essential technical indicators.In the data transformation procedure, one period of
stock data is selected as an experimental stock dataset. This dataset contains five daily fundamental stock quantities (maximum price, minimum price, opening price, closing price, and stock trading volume) and the daily price fluctuation, which
express the stock price change between any given day and the previous day (daily price fluctuation (t) = stock price
(t)stock price (t1)). The data of the five daily fundamental stock quantities is converted into the data of several popular
technical analysis indicators[26]: moving average (MA), momentum (MTM), stochastic %K(%K), stochastic %D(%D), relative
strength index (RSI), psychology line (PSY), Williams’ percent range (%R), volume ratio (VR), volume (Volume), and accumulative ratio (AR)[41].
In the procedure of selecting essential technical indicators, the popular indicators are analyzed by a ‘‘correlation matrix”
to examine their relationship degree to daily price fluctuations, and to select from the popular technical analysis indicators
those essential indicators which are highly related to daily price fluctuations. The selection approach employs a statistical
method, Pearson correlation with two-tailed tests, to select the essential technical analysis indicators. Pearson’s Correlation
Coefficient is usually signified byc. The statistical significance of ris tested using a t-test. The hypothesis for this test is:
H0: c¼0. A lowp-value for this test (less than 0.05, for example) means that there is sufficient evidence to reject the null
hypothesis in favor of the alternative hypothesis. For example, price fluctuation is related significantly withMA-5,MTM-5,
%K-5, %D-5,RSI-5,PSY-5, %R-5,VR-5, volume, andAR-5 (the marker ‘‘**” in the last column inTable 19).
3.2.1.2. Data discretization by CPDA and MEPA.In this procedure, two discretization methods, CPDA and MEPA, are utilized
to construct membership functions for these selected features and two numeric stock datasets (one dataset consisting of
Data transformation and select 
essential technical indicators 
Data discretization by CPDA and 
MEPA 
Rule generation by RST 
Accuracy and stock return 
improvement by GA 
Return calculation 
Evaluation and comparison 
Return 
calculation 
and 
performance 
evaluation 
Rule generation 
and rule refining 
Preprocess 
Fig. 4.The framework of proposed model.
1616
essential technical indicators, the other consisting of daily price fluctuations) are fuzzified into linguistic stock datasets (the
converted processes of daily price fluctuations, from numeric stock datasets to linguistic stock datasets, are demonstrated in
Table 8; the converted processes of a technical indicator, MA-5, from numeric stock datasets to linguistic stock datasets are
demonstrated inTable 10). The dataset of essential technical indicators is discretizated by MEPA and used as a conditional
attribute. The dataset of the daily price fluctuation is discretizated by CDPA and employed as a decision attribute.
3.2.2. Rule generation and rule refining
There are two operations contained in this phase, as follows:
3.2.2.1. Rule generation by RST.This procedure applies a toolset, based on RST (LEM2)[38,53], to extract preprocess phase
rules from the linguistic stock datasets, and to select the extracted rules with high support value as the initial population
for GA operations. To detail this procedure clearly, the computation steps are introduced inFig. 5.
3.2.2.2. Accuracy and stock return improvement by GA.This procedure employs GA to refine the extracted rules, thus, improving classification accuracy and stock return. To detail this procedure clearly, the computation steps are introduced inFig. 6.
3.2.3. Return calculation and performance evaluation
There are two processes contained in this phase, as follows:
3.2.3.1. Return calculation.Each selected experimental dataset is split into two subdatasets: training and testing datasets.
The refined rules, extracted by the proposed model from the training dataset, are used for forecasting the testing dataset
and calculating stock return, based on the trading strategies, as follows: (i) ‘‘buy on open and sell on close,” when the
selected rule indicates that the forecasted price fluctuation of the next day is ‘‘going up;” (ii) ‘‘sell on open and buy on close,”
when the selected rule indicates that forecasted price fluctuation of the next day is ‘‘going down;” and (iii) ‘‘no transaction,”
when the selected rule indicates that the forecasted price fluctuation of the next day is ‘‘staying flat.” Based on the refined
rules and the strategies, the returns for the proposed model can be calculated and summarized.
3.2.3.2. Evaluation and comparison.In this procedure, two types of performance evaluations, forecasting accuracy and stock
return, are employed. In forecasting accuracy evaluation, RST and GA models, using the same preprocess conditions as with
the proposed model, are employed as comparison models. In forecasting accuracy evaluation, the Buy-and-Hold method (defined in Eq.(21)), RST and GA models are employed as comparison models.
To detail the proposed model, each step of the proposed model is described, as follows:
Step 1:Data transformation and selection of essential technical indicators.
In this step, technical indicators are used as condition features, and the next-day price fluctuationðDPFnext dayÞ, defined in
Eq.(16), is used as a decision feature. The technical indicators are generated from five fundamental quantities (opening price,
highest price, lowest price, closing price and trading volume)[28,41]. In order to choose those essential technical indicators
High support value? 
Data input 
In put linguistic stock data with selected conditional attributes and 
decision attribute. 
Data mining 
Extract rules from linguistic stock dataset by the algorithms of RST. 
Selection 
Examine and choose the extracted rules with high support value as 
the rules of initial population. 
Coding rules into chromosome 
Code the rules of initial population into chromosome data for GA. 
Yes 
No  Remove the 
rules with low 
support value. 
Fig. 5.Rule generation by RST.
1617
as condition features that are highly related to the next-day price fluctuation, a correlation matrix is employed to select the
essential indicators from several popular indicators (seeTable 19).
Daily price fluctuationðtþ1Þ¼closing priceðtþ1Þopening priceðtþ1Þð16Þ
Step 2: Data discretization by CPDA and MEPA
In this step, CPDA is applied to discretize the next-day price fluctuation (decision attribute), and MEPA is used to discretize essential indicators (condition technical attributes). Because price fluctuations in the stock market and stock returns
follow normal distribution closely [3,47], CPDA is an appropriate method to discretize stock price data. In this model, the
next-day price fluctuation (decision attribute) is defined by three linguistic values:Up, FairandDown. Additionally, to partition the universe of discourse of each essential technical indicator based on its data characteristic, this step employs MEPA
to discretize condition features[11,12]. Granulating features is one important step for data-mining processes, especially for
RST, and by this step, the data dimensions of a database can be reduced and simplified.
In this paper, we discretize each condition attribute with 15 linguistic terms, because by using the TSMC as experimental
datasets, the accuracy of the proposed model performs best with 15 linguistic terms (seeTables 1 and 2), compared with 2, 3
and 7 linguistic terms.
Step 3:Rule generation by RST.
This step utilizes the algorithms of RST to mine rules from a training stock dataset. The extracted rules are in the form of
‘‘if-then” with specific condition attribute values and a decision attribute value, as follows:
Termination criteria satisfied
Initialization 
Generate an initial population with randomly generated chromosome. 
Evaluation 
Calculate the fitness values of all chromosomes. 
Selection 
Choose certain pairs of parents for producing offspring according to 
the selection method. 
Crossover 
Selected parents swap genes according to randomly generated 
crossover points. 
Mutation 
Selected parents randomly change one or more genes. 
No 
Stop 
The current chromosomes are the optimal solutions. 
YES 
Fig. 6.Accuracy and stock return improvement by GA operations.
Table 1
The accuracy of proposed model with different linguistic terms of condition feature for TSMC dataset (1999).
Linguistic terms of decision feature Linguistic terms of condition feature
23715
3
(Up, Fair, and Down)
0.278 0.316 0.5 0.55
1618
If RSI¼L8 andVolume; then DPFnext day¼Up
This rule states that if the linguistic value ofRSIisL8 (medium), and the linguistic value of theVolumeisL9 (more or less
high), then the next day price fluctuation isUp.
Step 4:Accuracy and stock return improvement by GA.
This step uses GAs to refine the extracted rules produced by RST from step 3 to improve forecasting accuracy and stock
return. The substeps of performance improvement are described below.
Step 4.1:Generate initial chromosomes.
The rules produced by RST are coded into chromosomes as an initial population, as inTable 3. Each condition feature is
coded with a value from ‘‘0” to ‘‘15,” where ‘‘0” signifies that the condition feature is not contained in the extracted rule, and
the coded values, from ‘‘1” to ‘‘15,” represent the linguistic value of this condition attribute, fromL1toL15, respectively.
Additionally, the decision feature is encoded from ‘‘1” to ‘‘3,” where ‘‘1” denotes that the daily price fluctuation of the next
day isDown, ‘‘2” Flat, and ‘‘3” Up.
The proposed model evaluates each chromosome by a user-defined fitness function, as shown in Eq.(17).
Fitness function¼
The number of observations classified correctly by the chromosome
All of observations in the training data
ð17Þ
Step 4.2:Perform genetic operations.
In this step, genetic operations (selection, crossover and mutation) are employed to refine the rules produced by RST from
step 3. In order to ensure the propagation of the elite chromosome, this step implements the genetic operations with the
Elitism mechanism[44,50]. This mechanism selects 0.2% of the individuals with the best fitness values to be the offspring
of the next generation, while the remaining individuals execute the genetic operations. Besides this, to enhance genetic operations in this substep, the rules with lower rule support value (rule support = 1) are removed.Table 4demonstrates the
parameter settings of GA in this substep.
Step 5:Return calculation.
This step calculates stock return by using the refined rules from step 4 in forecasting the stock price. The inference method based on the refined rule base is described in the following algorithm:
Algorithm 1.Return calculation
The initial forecasting price fluctuation (t+1) is set as‘‘Flat”
Dosearch each rule contained in the refined rule base
Ifthe linguistic values oftheactual essential technical indicators in the testing dataset at time t areequal tothe conditional
parts of the rule,thenthe linguistic value of the forecasting price fluctuation (t+1) is equal tothe decision part of the
rule
While not end of the refined rule base
There are three trading strategies provided in this step.
(1) ‘‘Buy on open and sell on close,” when the selected rule tells that the forecasting price fluctuation (t+1)isUp; (2) ‘‘sell
on open and buy on close,” when the forecasting price isDown; and (3) ‘‘no transaction,” when the forecasting price fluctuation isFlat.
Based on the inference method and trading strategies above, stock return is calculated by Eq.(18), when the forecasted
price fluctuation (t+1)isUp, or by Eq. (19), when the forecasted price fluctuation (t+1)isDown. In Eqs. (18) and (19), Unit
means the quantity of shares.
Table 2
The accuracy of proposed model with different linguistic terms of condition feature for TAIEX dataset (2000).
Linguistic terms of decision feature Linguistic terms of condition attribute
23715
3
(Up, Fair, and Down)
0.467 0.5 0.556 0.619
Table 3
The structure of the chromosomes for the proposed model.
Feature name Feature_1 Feature_2 Feature_n1 Feature_n DPFnextday
Coded value 0–15 0–15 0–15 0–15 1–3
1619
ReturnUpðtþ1Þ¼ðclosing priceðtþ1Þopening priceðtþ1ÞÞ unit ð18Þ
ReturnDownðtþ1Þ¼ðopening priceðtþ1Þclosing priceðtþ1ÞÞ unit ð19Þ
Step 6:Evaluation and comparison.
In this step, to evaluate forecasting performance carefully, accuracy and stock return are employed as performance indicators. This step calculates the stock return based on the three trading strategies above and sums up the stock return of all
transactions. The data-mining model’s accuracy is defined in Eq.(20).
AccuracyðTÞ¼
PjTj
i¼1
correct classificationðtiÞ
jTj
; ti 2T
Correct classificationðtiÞ¼
1; if classify ðtiÞ¼actual price fluctuationðtiÞ
0; otherwise
ð20Þ
whereTis the set of data instances that are classified by the proposed model,ti 2T; actual price fluctuationðtiÞis the classification for each data instance of actual price fluctuation labeled as one of three linguistic values,UpðL3Þ;FairðL2Þ, and Down
ðL1Þ; and classifyðtiÞreturns the classification of data instanceti
by the proposed model.
In a performance comparison, RST, GAs and the ‘‘Buy-and-Hold” approach are used as comparison methods to evaluate
the proposed model. To examine the performance difference between the proposed hybrid model and the data-mining models using a single method, RST[20,48]and GAs[2,28]are used as comparison models. Moreover, the ‘‘Buy-and-Hold” approach[8,40] is a common strategy for investors in the stock market, and therefore, this approach is used as another
comparison model. The stock return of the ‘‘Buy-and-Hold” approach is defined in Eq.(21), where Unitmeans the quantity
of shares.
ReturnBuy-and-hold¼ðclosing price
The last day of investing periodopening priceThe first day of investing periodÞunit ð21Þ
To detail the proposed model, an empirical case study is introduced in the following section.
3.3. Empirical case study
To demonstrate the proposed model clearly, in this section, a one-year period of Taiwan Semiconductor Manufacturing
Company (TSMC) stock data, from 1999/06/23 to 2000/05/11 (seeFig. 7, retrieved from Taiwan Stock Exchange Corporation
[54]), is employed as an experimental dataset to introduce the proposed algorithm step by step. Because the stock price on
the ‘‘ex-dividend day” fluctuates violently[19], this study removes the stock data of the ex-dividend day from the dataset
(the dataset selection is from 1999/06/23, the day after the ex-dividend day, to 2000/05/11, the day before the ex-dividend
day). The previous 10 months of stock data, from 1999/06 to 2000/03, is used for training, and the rest, from 2000/03 to
2000/05, is used for testing.
Fig. 7.The stock price of TSMC from 1999/06/23 to 2000/05/11.
Table 4
Parameter settings of GA.
Population size 1000
Number of generations 100
Initialization method Integer-encoding method
Percentage of elite 0.2
Selection method Tournament selection
Crossover method Uniform crossover
Crossover rate 0.8
Mutation method Single point mutation
Mutation rate 0.05
1620
By using the experimental stock dataset above, each step contained in the three forecasting phases of the proposed model
((I) Preprocess; (II) Rule generation and rule refining; and (III) Return calculation and performance evaluation) is introduced
and demonstrated, as follows:
Step 1:Data transformation and selection of essential technical indicators.
In this step, the five fundamental quantities of TSMC stock data (opening price, highest price, lowest price, closing price
and trading volume) are demonstrated asTable 5, and are transferred into popular technical indicators by their corresponding equations[28,41]. The eight essential technical indicators (condition features), selected by a correlation matrix for TMSC,
are described, as follows: accumulative ratio (AR), moving average (MA), psychology line (PSY), relative strength index (RSI),
stochastic %D(%D), stochastic %K(%K), volume, and Williams’ percent range (%R) (seeTable 6). The daily price fluctuation of
the next day (decision features) is produced by Eq.(16)(shown in the last column ofTable 6).
Step 2:Data discretization by CPDA and MEPA.
This step utilizes CPDA to discretize decision features and uses MEPA to discretize condition features. There are two substeps, as follows:
Use CPDA to discretize decision features
This substep uses CPDA to define the numeric intervals for three linguistic values,DownðL1Þ,FlatðL2Þ, andUpðL3Þ, used for
decision features (daily price fluctuation).Table 7lists the numeric intervals for the linguistic values. Based on these intervals, the membership function for the three linguistic values is established and shown inFig. 8. According to the membership
functions shown inFig. 8, three membership functions and three membership degrees are produced for each datum (daily
price fluctuation on the next day). In the fuzzification procedure, each datum is labeled as a linguistic value among three
linguistic values, based on the maximum membership degree. Table 8demonstrates the daily price fluctuation, the corresponding membership degrees for the three membership functions (lDown
;lFlat andlUp
Þ, and the labeled linguistic values
for the partial TSMC stock data.
Use MEPA to discretize condition features
Table 5
The partial five fundamental quantities of TSMC.
Date Opening price Highest price Lowest price Closing price Volume
1999/06/23 126.5 127 124 125 44,713
1999/06/24 124 130 123 129 69,778
1999/06/25 121 127.5 121 122.5 57,865
. . . . . .
2000/05/10 194 194 188 188 16,876
2000/05/11 182 184 177 179 29,310
2000/05/12 182 185 179 185 38,309
Table 6
The partial instances of forecasting technical indicators data.
Date MA-5 RSI-5 K-5 D-5 R-5 PSY-5 AR-5 Volume DPFnextday
1999/06/23 126 72.22 16.67 5.56 50.00 60 0.89 44,713 5
1999/06/24 127.6 72.22 44.44 18.52 0.00 60 1.13 69,778 1.5
1999/06/25 126.3 30.30 29.63 22.22 100.00 40 1.45 57,865 0
1999/06/28 125.4 34.48 19.75 21.40 100.00 40 2.69 29,340 1
. . . . . . . . . .
2000/05/08 190 50.00 63.97 54.75 0.00 40 2.22 14,605 0
2000/05/09 191 72.73 75.98 61.83 0.00 40 2.11 13,523 6
2000/05/10 191.2 53.33 50.65 58.10 100.00 40 1.25 16,876 3
2000/05/11 188.6 15.79 33.77 49.99 100.00 20 0.50 29,310 3
Table 7
The lower/upper boundary cumulative probability and linguistic intervals.
Linguistic value Cumulative probability Universe of discourseU
PLB PUB Lower boundary Midpoint Upper boundary Length of interval
Down(L1) 0 0.333 14.46 7.9 1.35 13.11
Flat(L2) 0.167 0.667 3.2 0.79 1.63 4.83
Up(L3) 0.5 1 0.14 10.3 20.46 20.32
1621
In this substep, the interval length of the 15 linguistic values for each condition feature is defined by MEPA (seeTable 9),
and thus, establishing the membership function of MEPA (seeFig. 9). InTable 10, the degree of membership for each datum
is calculated by the membership function of MEPA, and the last column is the linguistic value of the datum, which is fuzzified, based on the maximum membership of the datum.
From the results of two data discretization methods, CPDA and MEPA, the linguistic condition features and the decision
feature are demonstrated inTable 11.
Step 3:Rule generation by RST.
This step utilizes RST to construct decision rules from linguistic values in the above step (seeTable 11).Table 12shows
the partial rules and the rule support value. ‘‘Support” refers to how many records meet the generated decision rules in the
stock dataset. For example, ‘‘Rule 1: If AR-5 =L6 andPSY-5 =L9 andRSI-5 =L2 and Volume =L3 andK-5 =L7, then
DPFnext day= Up (support = 3)” indicates that there are three training records that meet the criteria of ‘‘Rule 1.”
-7.9  -0.79 10.3
-14.46 0.14 -3.2 1.63 -1.35
-20 -15 -10 -5 0 5 10
1 
0.5 
0 
L1 L2  L3
Daily price fluctuation 
Membership degree 
Fig. 8.Membership function of decision feature.
Table 8
The membership degree of decision feature based on CPDA.
Date Daily price fluctuation Membership degree for linguistic value Labeled linguistic value
ðDPFnext dayÞ lDown lFlat lUp
1999/06/23 5 0 0 0.48 Up
1999/06/24 1.5 0 0.05 0.13 Up
1999/06/25 0 0 0.67 0 Flat
. . . . . .
2000/05/08 0 0 0.67 0 Flat
2000/05/09 6 0.71 0 0 Down
2000/05/10 3 0.25 0.08 0 Down
2000/05/11 3 0 0 0.28 Up
Table 9
Linguistic intervals for 15 linguistic values produced by MEPA (MA-5).
Linguistic value Universe of discourse
Lower boundary Midpoint Upper boundary Length of interval
L1 104 123.1 125.7 21.7
L2 123.1 125.7 130.4 7.3
L3 125.7 130.4 136.05 10.35
L4 130.4 136.05 141.85 11.45
L5 136.05 141.85 155.3 19.25
L6 141.85 155.3 155.9 14.05
L7 155.3 155.9 157.4 2.1
L8 155.9 157.4 177.8 21.9
L9 157.4 177.8 184.7 27.3
L10 177.8 184.7 190.2 12.4
L11 184.7 190.2 208.6 23.9
L12 190.2 208.6 210.1 19.9
L13 208.6 210.1 211.2 2.6
L14 210.1 211.2 213.3 3.2
L15 211.2 213.3 215 3.8
Notes:L1 is very very very very very low,L2 is very very very very low,L3 is very very very low,L4 is very very low,L5 is very low,L6 is low,L7 is more or
less low,L8 is medium,L9 is more or less high,L10 is high,L11 is very high,L12 is very very high,L13 is very very very high,L14 is very very very very high,
L15 is very very very very very high.
1622
Step 4:Accuracy and stock return improvement by GAs.
This step uses genetic algorithms (GAs) to improve the accuracy and stock return of rules that are produced by RST. There
are two substeps in this step, as follows:
Step 4.1:Generate initial chromosomes.
This substep encodes each rule that is produced by RST in Step 3 as a chromosome in an initial population and evaluates
each chromosome in each population using Eq.(17). For example, this substep encodes Rule 1 in Table 12into a chromosome, as shown inTable 13.
InTable 13, the coded value of RSI-5 is ‘‘2,” which represents that the linguistic value ofRSI-5 isL2. In the same way, the
coded values ofK-5,PSY-5,AR-5 andVolumeare 7, 9, 6 and 3, which show that the linguistic values areL7,L9,L6 and L3,
respectively. The coded values forMA-5, D-5 andR-5 are ‘‘0,” which denote that the rule does not contain the three condition
features. Further, the forecasting stock price,DPFnextday, means ‘‘Up” because the coded value is ‘‘3” (1 forDown, 2 for Fair,3
forUp). In addition, the proposed model calculates a fitness value to evaluate each chromosome by Eq.(17).
Step 4.2: Perform genetic operations.
This substep refines the initial rules produced by using genetic operators, such as selection, crossover and mutation.Table
14shows the partial rules refined by GAs and the rule support.
In this paper, the proposed model employs a rule-filter, which selects useful rules for which rule support is greater than 1,
and which deletes rules with low rule support (rule support = 1). Moreover, genetic algorithms and the proposed model utilize the same rule-filter condition (i.e., rule support is more than 1), the parameter settings of which are shown in Table 4.
Fig. 9.Membership functions for 15 linguistic values using the attribute of MA-5.
Table 10
The partial MEPA membership degrees of MA-5 feature for TSMC.
Date Technical indicator
value (MA-5)
Membership degree for linguistic value Labeled
linguistic
value
lL1 lL2 lL3 lL4 lL5 lL6 lL7 lL8 lL9 lL10 lL11 lL12 lL13 lL14 lL15
1999/06/23 126 0 0.94 0.06 0 0 0 0 0 0 0 0 0 0 0 0 L2
1999/06/24 127.6 0 0.6 0.4 0 0 0 0 0 0 0 0 0 0 0 0 L2
1999/06/25 126.3 0 0.87 0.13 0 0 0 0 0 0 0 0 0 0 0 0 L2
1999/06/28 125.4 0.12 0.88 0 0 0 0 0 0 0 0 0 0 0 0 0 L2
. . . . . . . . . . . . . . . . . .
2000/05/08 190 0 0 0 0 0 0 0 0 0 0.04 0.96 0 0 0 0 L11
2000/05/09 191 0 0 0 0 0 0 0 0 0 0 0.96 0.04 0 0 0 L11
2000/05/10 191.2 0 0 0 0 0 0 0 0 0 0 0.95 0.05 0 0 0 L11
2000/05/11 188.6 0 0 0 0 0 0 0 0 0 0.29 0.71 0 0 0 0 L11
Note: LV donates linguistic value.
1623
Step 5:Return calculation.
This step calculates the stock return by using the rules produced from step 4 in forecasting stock prices. The stock return
is compared with the listed model in the next step.
Step 6:Evaluation and comparison.
To evaluate the proposed model, the accuracy and stock return of the proposed model are compared with those of the
three listed methods: RST, GAs and the ‘‘Buy-and-Hold” approach (seeTable 15). The accuracy and stock return for the comparison models and the proposed model are listed inTable 16, from which we can see that the proposed model outperforms
the listed models.
Table 11
The partial linguistic value of TSMC.
Date MA-5 RSI-5 K-5 D-5 R-5 PSY-5 AR-5 Volume DPFnextday
1999/06/23 L2 L10 L3 L1 L9 L11 L6 L14 Up
1999/06/24 L2 L10 L7 L4 L1 L11 L6 L15 Up
1999/06/25 L2 L1 L7 L4 L15 L9 L7 L15 Flat
1999/06/28 L2 L2 L3 L4 L15 L9 L8 L6 Flat
. . . . . . . . . .
2000/05/08 L11 L2 L8 L6 L1 L9 L7 L2 Flat
2000/05/09 L11 L11 L12 L6 L1 L9 L7 L2 Down
2000/05/10 L11 L2 L8 L6 L15 L9 L7 L2 Down
2000/05/11 L11 L1 L7 L6 L15 L8 L4 L6 Up
Table 12
The partial rules generated by rough set theory.
No. Rules Rule support
1IfAR-5 =L6 andPSY-5 =L9 andRSI-5 =L2 andVolume=L3 andK-5 =L7 thenDPFnextday¼Up 3
2IfR-5 =L1 andAR-5 =L7 andRSI-5 =L13 andK-5 =L13 thenDPFnextday¼Up 3
3IfAR-5 =L6 andPSY-5 =L11 andMA-5 =L2 thenDPFnextday¼Up 3
4IfR-5 =L15 andRSI-5 =L1 andK-5 =L2 andMA-5 =L11 thenDPFnextday¼Up 3
. . .
60 If PSY-5 =L9 andAR-5 =L6 andVolume=L2 andMA-5 =L5 andRSI-5 =L8 thenDPFnext day¼Down 1
61 If AR-5 =L7 andPSY-5 =L11 andMA-5 =L4 andRSI-5 =L10 thenDPFnext day¼Down 1
62 If MA-5 =L12 andVolume=L1 andRSI-5 =L11 thenDPFnext day¼Down 1
63 If RSI-5 =L1 andD-5 =L5 andMA-5 =L12 andK-5 =L6 thenDPFnext day¼Down 1
Table 13
The structure of the chromosomes.
Feature name MA-5 RSI-5 K-5 D-5 R-5 PSY-5 AR-5 Volume DPFnext day
Coded value 0 2 7 0 0 9 6 3 3
Note: The values of each condition features: 1 represent that the linguistic value isL1, and so on.
The values ofDPFnext day:1isDown,2isFlat,3isUp.
Table 14
The partial rules refined by genetic algorithms.
No. Rules Rule Support
1IfMA-5 =L8 andK-5 =L1 andR-5 =L15 thenDPFnext day¼Down 26
2IfMA-5 =L8 andK-5 =L1 andD-5 =L7 thenDPFnext day¼Down 22
3IfK-5 =L1 andPSY-5 =L9 andAR-5 =L15 thenDPFnext day¼Up 20
4IfD-5 =L9 andR-5 =L1 andVolume=L2 thenDPFnextday¼Up 19
. . .
281 If RSI-5 =L15 andD-5 =L15 andAR-5 =L15 thenDPFnext day¼Flat 1
282 If D-5 =L8 andR-5 =L1 andPSY-5 =L8 thenDPFnext day¼Down 1
283 If D-5 =L4 andR-5 =L15 andVolume=L2 thenDPFnext day¼Down 1
284 If RSI-5 =L8 andR-5 =L1 andPSY-5 =L9 andVolume=L2 thenDPFnext day¼Up 1
1624
4. Model verification
To verify the proposed model, this section provides two types of performance evaluations: (I)Forecasting accuracy evaluation: produce the accuracy of the proposed model based on Eq.(20)and provide two other comparison models, which use
only one data-mining method, RST or GA, to produce forecasts under the same preprocess conditions as those of the proposed model; and (II)Stock return evaluation: produce the stock return based on Eqs.(18) and (19), and provide three other
comparison models: Buy-and-Hold (defined in Eq.(21), RST and GAs.
In this experiment, a six-year period of the TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) stock
index, from 2000/01/04 to 2005/12/30, was selected as an experimental database, and was divided into 6 datasets by year.
The previous 10-month period of the stock index, from January to October, was used for training, and the rest, from November to December, was used for testing.
The accuracy for the three models (RST, GAs and the proposed model) is listed asTable 17, and the comparisons show that
the proposed model outperforms the other two listed models. Further, from the stock return comparisons shown inTable 18,
Table 15
The stock returns of ‘‘Buy-and-Hold” in testing period.
Data period Opening price Closing price Buy-and-Hold return (unit)
2000/03/22–2000/05/11 194 179 15
Note:Unitmeans the quantity of share.
Table 16
The forecasting performance comparison for TSMC.
Data period Accuracy Stock return (unit)
Rough set Genetic algorithms Proposed model Buy-andHold
Rough set Genetic algorithms Proposed model
2000/03/22–2000/05/
11
0.545 0.42 0.55 15 15 10 16
Note: Some literatures accept the accuracy rate which less than or close to 0.5 in forecasting price fluctuation of stocks[8,30].
Table 17
The accuracy comparisons for three models (TAIEX).
Year Model
Rough set theory Genetic algorithms Proposed model
2000 0.602 0.574
a
0.619
2001 0.615 0.581 0.628
a
2002 0.53 0.523 0.593
a
2003 0.512 0.535 0.582
a
2004 0.571 0.556 0.614
a
2005 0.488 0.51 0.568
a
Average 0.553 0.547 0.601
a
a
Maximum accuracy among three models.
Table 18
The stock returns comparisons for four models (TAIEX,unit).
Year Model
Buy-and-Hold Rough set theory Genetic algorithms Proposed model Profit order
2000 813.21 1590.68 1817.29
a
2271.03 1
2001 1612.16 923.9 1272.05 1683.51
a
2
2002 144.24 304.28 353.56 421.82
a
4
2003 163.62 70.78 247 336.25
a
5
2004 414.04 196.06 481.65 780.26
a
3
2005 745.09
a
105.85 163.8 210.83 6
Average 275.04 531.93 722.56 950.62
a
Note:Unitmeans the quantity of one share.
a
Maximum return among four models.
1625
Table 19
Correlations of technical indicators for TAIEX.
MA-5 MTM-5 %K-5 %D-5 RSI-5 PSY-5 %R-5 VR-5 Volume AR-5 Price fluctuation
MA-5 Pearson correlation 1 .741
***
.753
***
.472
***
.797
***
.818
***
.835
***
.676
***
1.000
***
.251
***
.169(
***
)
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .009
MTM-5 Pearson correlation .741
***
1 .903
***
.714
***
.880
***
.889
***
.713
***
.861
***
.741
***
.299
***
.112
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .088
%K-5 Pearson correlation .753
***
.903
***
1 .860
***
.835
***
.836
***
.781
***
.768
***
.753
***
.223
***
.133(
**
)
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .001 .042
%D-5 Pearson correlation .472
***
.714
***
.860
***
1 .713
***
.705
***
.424
***
.585
***
.472
***
.074 .134(
**
)
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .260 .041
RSI-5 Pearson correlation .797
***
.880
***
.835
***
.713
***
1 .973
***
.619
***
.791
***
.797
***
.232
***
.152(
**
)
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .020
PSY-5 Pearson correlation .818
***
.889
***
.836
***
.705
***
.973
***
1 .627
***
.796
***
.818
***
.269
***
.128(
**
)
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .047
%R-5 Pearson correlation .835
***
.713
***
.781
***
.424
***
.619
***
.627
***
1 .594
***
.835
***
.232
***
.126(
**
)
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .049
VR-5 Pearson correlation .676
***
.861
***
.768
***
.585
***
.791
***
.796
***
.594
***
1 .676
***
.367
***
.109
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .097
Volume Pearson correlation 1.000
***
.741
***
.753
***
.472
***
.797
***
.818
***
.835
***
.676
***
1 .251
***
.169
***
Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000 .000 .009
AR-5 Pearson correlation .251
***
.299
***
.223
***
.074 .232
***
.269
***
.232
***
.367
***
.251
***
1 .137(
**
)
Sig. (2-tailed) .000 .000 .001 .260 .000 .000 .000 .000 .000 .035
Price fluctuation Pearson correlation .169
***
.112 .133(
**
) .134(
**
) .152(
**
) .128(
**
) .126(
**
) .109 .169
***
.137(
**
)1 Sig. (2-tailed) .009 .088 .042 .041 .020 .047 .049 .097 .009 .035
Notes:MA-5 denotes that the value of the indicator is calculated using five periods of fundamental stock quantities (maximum price, minimum price, opening price, closing price, and stock trading volume) from
present day to previous 4 day; and the values of other indicators (MTM-5, %K-5, %D-5,RSI-5,PSY-5, %R-5,VR-5 andAR-5) are produced in the same way.
**
Denotes that correlation is significant at the 0.05 level using 2-tailed test.
***
Denotes that correlation is significant at the 0.01 level.
1626 C.-H. Cheng et al. / Information Sciences 180 (2010) 1610–1629
it is clear that the proposed model surpasses the other three models (Buy-and-Hold, RST and GAs) in each testing period,
except 2005. These stock return evaluations demonstrate the outstanding performance of the proposed model.
5. Findings and conclusions
This paper has proposed a new hybrid model, based on four novel methods (CDPA, MEPA, RST and GA), to promote stock
market forecasting performance. From the performance evaluation data in the above section, we can conclude that the main
objective of this paper has been reached. Furthermore, by examining the performance data carefully, we also ascertain that
four important findings for the proposed model emerge, as follows:
(1) The proposed model produces a positive stock return, whether the market is bullish or bearish.
Based on the stock return for the Buy-and-Hold approach (seeTable 18), it has been shown that, from 2000 to 2005,
there were three bear markets (2000, 2002, and 2003) and three bull markets (2001, 2004, and 2005). From the stock
return evaluations shown inTable 18, it is clear that the proposed model produces a positive stock return for each
dataset. This evidence points to the exceptional ability of the proposed model to mine correct price patterns in the
stock market.
(2) The proposed model performs outstandingly when the stock market is in a nearly complete bull market (upside trend)
or bear market (downside trend).
Figs. 10 and 11show that the price trends of the TAIEX were mostly downward in 2000 and upward in 2001. From
Table 18, it can be observed that the stock return of the proposed model in 2000 is the best (2271.03) among the
six datasets and much better than the other three models (813.21 for Buy-and-Hold, 1590.68 for RST, and
1817.29 for GA). In 2001, the stock return of the proposed model is in second place (1683.51), better than the other
three models (1612.16 for Buy-and-Hold, 923.9 for RST, and 1272.05 for GA). Despite the ‘‘Buy-and-Hold” approach
TAIEX_2000
0
2.000
4.000
6.000
8.000
10.000
12.000
Stock index 
2000/01/04 2000/04/13 2000/07/14 2000/10/13 Date 
Fig. 10.The actual stock index for the TAIEX in 2000.
TAIEX_2001
0
2.000
4.000
6.000
8.000
Stock index 
2001/01/02 2001/04/20 2001/08/01 2001/11/14 Date 
Fig. 11.The actual stock index for the TAIEX in 2001.
TAIEX_2005
5.000
5.500
6.000
6.500
7.000
Stock index 
2005/01/03 2005/04/21 2005/08/01 2005/11/10 Date 
Fig. 12.The actual stock index for the TAIEX in 2005.
1627
making a good stock return when the stock market was in a pure upward trend in 2001, the proposed model still surpasses this approach. These performance evaluations prove that the proposed model can extract tinier fluctuations in
the stock price than the other three models when the stock market is in an almost pure bull market or bear market.
(3) The three listed data-mining models (RST, GAs and the proposed model) perform their worst when there are many
violent fluctuations occurring in the stock market.
Fig. 12shows that the TAIEX fluctuated violently in 2005. The performance evaluations (seeTables 17 and 18) show
that the worst case of the proposed model occurred for 2005. This can be explained by the fact that there were many
conflicting rules extracted from the unstable market, which contained many violent fluctuations, and therefore, the
performance value of the proposed model was dramatically reduced. Additionally, this phenomenon also occurred
in RST and GA.
(4) Integrating RST and GA together in forecasting processes can produce a positive effect, enhancing model performance.
In the overall performance evaluation of accuracy (see Table 17), RST (0.553) proves marginally better than GAs
(0.547), which means that RST can produce more effective rules than GAs. However, in the overall performance evaluation of stock return (seeTable 18), GAs (722.56) are much better than RST (531.93), which tells that GAs can deal
with the price variations in the stock market better than RST. FromTables 17 and 18, we can see that the proposed
hybrid model (0.601, 950.62) performs much better than RST (0.553, 531.93) and GA (0.547, 722.56) in accuracy
and stock return. The evidence demonstrates that the proposed hybrid model can acquire the advantages from the
two data-mining methods (RST and GA) and therefore, produce superlative results in forecasting the stock market.
Besides these findings, by implementing this experiment, two advantages were discovered for the proposed model: (1)
the proposed model can produce more reasonable and understandable rules, because the ‘‘if-then” rules produced by
RST can model the qualitative aspects of human knowledge; and (2) the proposed model can provide stock investors
with objective suggestions (forecasts) to make investment decisions in the stock market, because the proposed model
produces forecasting rules based on objective stock data rather than subjective human judgments.
For future research, two approaches to refine the proposed model, in order to improve forecasting performance, are suggested: (1) employ other data discretization methods in the preprocessing phase; and (2) use other artificial intelligence
algorithms in the forecasting process.
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