程序代写代做代考 AI algorithm finance Bayesian Microsoft Word – S. Parasuraman.doc
Microsoft Word – S. Parasuraman.doc
Abstract—In this paper, we propose a hybrid machine learning
system based on Genetic Algorithm (GA) and Support Vector
Machines (SVM) for stock market prediction. A variety of indicators
from the technical analysis field of study are used as input features.
We also make use of the correlation between stock prices of different
companies to forecast the price of a stock, making use of technical
indicators of highly correlated stocks, not only the stock to be
predicted. The genetic algorithm is used to select the set of most
informative input features from among all the technical indicators.
The results show that the hybrid GA-SVM system outperforms the
stand alone SVM system.
Keywords—Genetic Algorithms, Support Vector Machines,
Stock Market Forecasting.
I. INTRODUCTION
TOCK market prediction is regarded as a challenging task
in financial time-series forecasting. This is primarily
because of the uncertainties involved in the movement of the
market. Many factors interact in the stock market including
political events, general economic conditions, and traders’
expectations. Therefore, predicting market price movements is
quite difficult. Increasingly, according to academic
investigations, movements in market prices are not random.
Rather, they behave in a highly non-linear, dynamic manner.
Also, the ability to predict the direction and not the exact
value of the future stock prices is the most important factor in
making money using financial prediction. All the investor
needs to know to make a buying or selling decision is the
expected direction of the stock. Studies have also shown that
predicting direction as compared to value can generate higher
profits [1].
The rest of this paper is organized as follows: In section 2,
we give an overview of previous studies in this area. In
sections 3 and 4, we give a brief introduction to the basic
concepts behind the theory of technical analysis and SVM
respectively. In section 5, the stock prediction problem is
explained. In section 6, we describe our proposed system. In
section 7, the experimental results are given. Conclusions and
directions for further work are given in section 8.
Manuscript received March 29, 2008. Rohit Choudhry is a Masters’
student at the Electronics & Computer Engineering Department, Indian
Institute of Technology Roorkee, India (e-mail: rohetuec@iitr.ernet.in).
Kumkum Garg is Professor at the Electronics & Computer Engineering
Department, Indian Institute of Technology Roorkee, India (e-mail:
kgargfec@iitr.ernet.in).
II. RELATED RESEARCH
A number of artificial intelligence and machine learning
techniques have been used over the past decade to predict the
stock market. Neural Networks are by far the most widely
used technique. Time Delay Neural Networks have been used
in [2] for stock market trend prediction. Probabilistic Neural
Networks have been used in [3] to model it as a classification
problem, the 2 classes being a rise or a fall in the market.
Recurrent Neural Nets have been used in [4] for predicting the
next day’s price of the stock index. Other methods that have
been used to forecast the stock market include Bayesian belief
networks [5], evolutionary algorithms [6] [7], classifier
systems [8], and fuzzy sets [9].
Recent research tends to hybridize other AI techniques with
ANN. Kim & Shin [10] have proposed a hybrid model of
Genetic Algorithms and Neural Networks for optimization of
the number of time delays and network architectural factors
using GA, to improve the effectiveness of constructing the
ANN model. The study in [11] integrated the rule-based
technique and ANN to predict the direction of change of the
S&P 500 stock index futures on a daily basis. Kohara et al
[12] incorporated prior knowledge in ANN to improve the
performance of stock market prediction.
In the last few years, the use of SVMs for stock market
forecasting has made significant progress. SVMs were first
used by Tay & Cao for financial time series forecasting [13],
[14], [15]. Kim has proposed an algorithm to predict the stock
market direction by using technical analysis indicators as
input to SVMs [16]. Studies have compared SVM with Back
Propagation Neural Networks (BPN). The experimental
results showed that SVM outperformed BPN most often
though there are some markets for which BPN have been
found to be better [17]. These results may be attributable to
the fact that the SVM implements the structural risk
minimization principle and this leads to better generalization
than Neural Networks, which implement the empirical risk
minimization principle.
III. TECHNICAL ANALYSIS
Technical analysis is the study of market action using past
prices and trading volumes for the purpose of forecasting
future price trends. Technical analysis assumes that stock
prices move in trends, and that the information which affects
prices enters the market over a finite period of time, not
instantaneously. Technical analysis contradicts the long held
Efficient Market Hypothesis (EMH). EMH states that market
A Hybrid Machine Learning System for Stock
Market Forecasting
Rohit Choudhry, and Kumkum Garg
S
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prices follow a random walk and cannot be predicted based on
their past behavior. According to EMH, all information that
enters the market affects the prices instantaneously. If the
EMH were true, it would not be possible to use AI techniques
to predict the market. However, due to the success of technical
analysts in the financial world and a number of studies
appearing in academic literature successfully using AI
techniques to predict the market, EMH is widely believed to
be a null hypothesis now.
Technical analysts make use of technical indicators, which
are mathematical formulations which give us clues about the
trend of the market. An example of a technical indicator is the
famous stochastic oscillator %K:
%K = (P(c) – P (l))/(P(h) – P(l))
where P(c), P (h), and P (l) represent closing price, highest
price and lowest price of a security over any time period.
Technical analysts normally use a number of such indicators
and judgment gained from experience to decide which pattern
a particular instrument reflects at a given time, and what the
interpretation of that pattern should be. Technical analysts
may disagree among themselves over the interpretation of a
given chart. These technical indicators have been successfully
used as input features to AI techniques, for example, in [16].
IV. SUPPORT VECTOR MACHINES
The Support Vector Machines (SVMs) were proposed by
Vapnik [18]. SVMs are a type of maximum margin classifiers.
They seek to find a maximum margin hyperplane to separate
the classes, i.e., they maximize the distance of the hyperplane
from the nearest training examples. The hyperplane thus
obtained is called the optimal separating hyperplane (OSH)
and the training examples that are closest to the maximum
margin hyperplane are called support vectors.
If the data is linearly separable, a hyperplane separating the
binary decision classes in the two attribute case can be
represented as the following equation:
y = w0 + w1x1 + w2x2 (1)
where y is the outcome, xi are the attribute values, and there
are three weights wi to be learned by the learning algorithm.
The maximum margin hyperplane can be represented as the
following equation in terms of the support vectors:
y = b + ∑αiyix(i).x (2)
where y is the class value of training example x(i), the vector
x represents a test example, the vectors x(i) are the support
vectors and · represents the dot product.. In this equation, b
and αi are parameters that determine the hyperplane. Finding
the support vectors and determining the parameters b and αi is
equivalent to solving a linearly constrained quadratic
programming problem.
If the data is not linearly separable, as in this case, SVM
transforms the inputs into the high-dimensional feature space.
This is done by using a kernel function as follows:
y = b + ∑αiyiK(x(i),x) (3)
There are many different kernels for generating the inner
products to construct machines with different types of
nonlinear decision surfaces in the input space. Common
examples of the kernel function are the polynomial kernel
K(x; y) = (xy+1)n and the Gaussian radial basis function(RBF)
K(x; y) = exp(−1/δ2(x − y)2) where n is the degree of the
polynomial kernel and δ2 is the bandwidth of the Gaussian
RBF kernel.
A unique feature of SVMs is that they are resistant to the
over-fitting problem. This is because while many traditional
neural network models have implemented the empirical risk
minimization principle, SVM implements the structural risk
minimization principle. The former seeks to minimize the
misclassification error or deviation from correct solution of
the training data, but the latter searches to minimize an upper
bound of generalization error.
V. THE STOCK DIRECTION PREDICTION PROBLEM
The stock market direction problem is modeled as a two
class classification problem. The directions are categorized as
0 & 1 in the data. A class value of 0 means that the present
day’s price is less than the previous day, i.e., a fall in the
stock, and a class value of 1 means that the present day’s price
is more than the previous day, i.e., a rise in the stock price.
We chose the Indian stock market for the study. In the past,
most of the work in this area has focused on the American and
Korean stock markets; there exists little published work using
an AI technique for predicting the Indian market. This is
significant as studies have shown that different stock markets
have different characteristics and results obtained for one are
not necessarily true for another [17]. In the Indian stock
market, we have chosen 3 stocks; Tata consultancy services
(TCS), Infosys, and Reliance industries limited (RIL) for our
experiments as these are the most prominent stocks on India’s
stock exchange.
VI. PROPOSED SYSTEM
A. Correlation between Stocks
Studies have shown that the price of a stock does not move
in isolation. There is statistically significant correlation
between prices of certain stocks and thus, price movements in
one stock can often be used to predict the movement of other
stocks [19] [20].
Let the two stocks whose correlation we want to find be
denoted by S and T. The correlation between these stocks is
given by:
Cor(S, T) = ∑ ((S (i) – SA) (T (i) – TA))/ (σSσTn)
where S(i) & T(i) are closing prices of the stock on the ith
day, SA & TA are the mean prices of the stocks, σS and σT are
the standard deviations, and n is the number of days over
which the correlation is to be found.
As an example, Fig. 1 shows five companies having the
highest absolute value of correlation with TCS, which is a
major IT services provider and a part of the Tata
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conglomerate. It can be seen that the companies having the
highest level of correlation with TCS are the ones which are in
the same industry or a part of the same group; a result that was
expected.
Tata Consultancy Services – An IT services firm
Highly Correlated Companies:
• Infosys Technologies – An IT services firm
• Wipro Technologies – An IT services firm
• Tata Motors – A motor company, also part of the
Tata group
• Bharti – India’s largest telecom company
Fig. 1 Correlation example of a company
B. Input Features
Technical analysts make use of technical indicators, which
are mathematical formulations which give us clues about the
trend of the market. We use a set of 35 such technical
indicators as candidates for input features that are being used
by financial experts [21]. Some of the more important features
are given in Table I.
We first find the m companies which exhibit the highest
correlation with the stock to be predicted. One of these m
stocks will always be the target stock itself as it will have
perfect correlation with itself. Then, these 35 features are
calculated for each of these m companies by using their past
prices and trading volumes. Thus, we obtain a set of 35*m
candidate features.
C. Genetic Algorithm
As explained above, we obtain a set of 35*m candidate
features. A Genetic Algorithm is now used to select a set of
salient features from among them. The selected features are
used as inputs to a Support Vector Machine. The purpose here
is to obtain an optimal subset of features which produce the
best possible results. The various steps in the GA are
described below:
• Representation: We represent a chromosome by a binary
vector of size 35*m, where each bit of the chromosome
tells whether the corresponding input feature is selected
or not.
• Fitness Evaluation: The following fitness function is
used for evaluating the fitness of a chromosome i:
fitness = (A(i) – AR)/( ∑ (A(i) – AR) )
where, A(i) is the classification accuracy obtained by the
SVM with the input feature set as described
by chromosome I and AR is the accuracy of a random
guess, which, in this case is 0.5.
• Selection: Roulette Wheel selection is used for parent
selection. Thus, chromosomes with high fitness scores get
selected more often.
• Crossover and Mutation are then carried out to produce
a new generation.
• Stopping Condition: The GA stops when it does not
find a better solution for a fixed number of generations.
D. Support Vector Machine
The optimal set of features as selected by the genetic
algorithm above is then used as input to the SVM. The
original input features are scaled into the range of [−1,1]. The
goal of linear scaling is to independently normalize each
feature component to the specified range. It ensures the larger
value input attributes do not overwhelm smaller value inputs,
and thus helps to reduce prediction errors. The SVM Light
software package [22] was used to perform the experiment.
The kernel function used for transforming the input space to
the higher dimension space is the Gaussian radial basis
function kernel. This kernel function was selected as it gave
better experimental results than the other common kernel
functions.
TABLE I
SOME OF THE INPUT FEATURES AND THEIR FORMULAS
Feature Name Formula
Momentum (C(i)/C(i-N))* 100
Williams %R (HH(n)-C(t))/
(HH(n)-LL(n))*100
Rate of Change (ROC) (C(t) – C(t-n))/C(t-n)
5 Day Disparity (C(t)/MA(5))*100
10 Day Disparity (C(t)/MA(10))*100
Stochastic %K (C(t) – L(t))/(H(t) – L(t))
Price Volume Trend
(PVT)
((C (t) – C (t-1)) / C(t-1)) *
V
VII. EXPERIMENTAL RESULTS
We tested our approach with three stocks, TCS, Infosys and
RIL as mentioned above. The data used for this study were
obtained from the Yahoo Finance website [23]. We collected
in all 1386 trading days’ data from August 12, 2002 to
January 18, 2008. For each day, the opening, highest, lowest
and closing values of the stock price were obtained. Further,
the trading volumes were also obtained. The data were
collected for the 30 companies which comprise the Bombay
Stock Exchange’s representative index ‘Sensex’. 60% of the
data was used for training, 20% for validation and 20% for
testing the system.
The prediction performance is measured in terms of ‘hit
ratio’, which is the percentage of times our system’s
prediction for direction was correct. The results of our
approach were compared with the results obtained by the
stand alone SVM, where the 35 features for the target
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company alone are used as input. The results of the stand
alone SVM were found to match very closely with the results
reported by Kim [16] for a similar model. Also, our GA-SVM
hybrid model significantly outperformed the SVM. For
example, for TCS, the hit ratio of our GA-SVM was
61.7328% while that of the SVM was found to be 58.0903%.
The hit ratios for all the three stocks are given in Table II.
TABLE II
HIT RATIOS OF SVM AND GA-SVM (%)
VIII. CONCLUSION
In this paper, we proposed a hybrid GA-SVM system for
predicting the future direction of stock prices. A set of
technical indicators, obtained from the stock to be predicted,
and also from the stocks exhibiting high correlation with that
stock were used as input features. The results showed that the
correlation concept & the GA helped in improving the
performance of the SVM system significantly.
There is a lot of scope for further work in this area. If
various political & economic factors which affect the stock
market are also taken into consideration other than the
technical indicators as input variables, better results may be
obtained. Also, incorporating market specific domain
knowledge into the system might help in achieving better
performance.
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SVM GA-SVM
TCS 58.09 61.732
Infosys 56.748 60.285
Reliance 55.643 59.534
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