A LINEAR REGRESSION APPROACH TO PREDICTION OF STOCK MARKET TRADING VOLUME: A CASE STUDY

International Journal of Managing Value and Supply Chains (IJMVSC) Vol.4, No. 3, September 2013
DOI: 10.5121/ijmvsc.2013.4303 25
A LINEAR REGRESSION APPROACH TO PREDICTION
OF STOCK MARKET TRADING VOLUME: A CASE
STUDY
Farhad Soleimanian Gharehchopogh1
, Tahmineh Haddadi Bonab2
and Seyyed Reza Khaze3
1
Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia,
Iran
2
Department of Computer Engineering, Science and Research Branch, Islamic Azad
University, West Azerbaijan, Iran
3
Department of Computer Engineering, Dehdasht Branch, Islamic Azad University, Iran,
ABSTRACT
Predicting daily behavior of stock market is a serious challenge for investors and corporate stockholders
and it can help them to invest with more confident by taking risks and fluctuations into consideration. In
this paper, by applying linear regression for predicting behavior of S&P 500 index, we prove that our
proposed method has a similar and good performance in comparison to real volumes and the stockholders
can invest confidentially based on that.
KEYWORDS
Stock Market, Stock index, S&P 500, Data Mining, Regression, Dataset
1. INTRODUCTION
Predicting the stock market due to its importance and popularity among the masses and also small
and large companies due to financial benefits and its low risk is a growing topic in research [1].
Despite the risk of falling too much value per share due to market fluctuations rarely happens, but
again, the risk is there. These fluctuations which effect on stock price and trading volume have
some difficulties in predicting. The fluctuations effect on the behavior of people in terms of
capital savings or investment, the stock price and the increase or decrease of risk for investors.
Therefore in general, predicting the stock market behavior through techniques and various
methods is a useful tool to assist investors to act with greater certainty and taking the risks and
volatility of an investment into consideration and know when to buy the cheapest price and when
to sell to highest price [2].
Data mining techniques have a more successful performance in predicting various fields such as
economy, policy and engineering compared to traditional statistical methods by discovering
hidden knowledge of data [3, 4, and 5]. Experience has shown that machine learning techniques
could be successful in predicting daily stock price and its trading volume [6]. In this paper, at first
review the prior researches done for predicting stock market and then we describe the importance
of trading volume. By using linear regression we predict S&P 500 index [7] behavior and at the
end we compared and evaluated the result of our proposed method with other approaches.

26
2. PREVIOUS WORK
Nowadays the stock market has been called for research in many fields due to its effects on
financial challenging and capacity of predicting its various aspects through different scientific
methods such as genetic algorithm, Artificial Neural Network (ANN) and other Meta heuristic
algorithms. Many institution and academic researchers are trying to propose a method for
predicting next day behaviors of stock indexes in order to be better than the other methods, like a
research that Majhi and other friends [8] did via applying bacterial foraging optimization
technique for predicting stock market and S&P500 indexes in short and long terms, and they
made a linear combiner model which its weights updated by BFO and comparing it with Multi-
Layer Perceptron (MLP) based method showed that Majhi and other friend's method has less
calculative complexity and more precision to MLP method.
Another predicting system [9] in which counting of complex keyword topples and its
transformation to predict stock market behavior periodically and doing real-time forecasting on
web has been done. Some researchers used text mining approach [10], their findings investigates
effects of financial news in predicting stock market. Increasing social networks and their
popularity among people have been led into new ideas of investigating of effect of the popularity
and application of these social networks that can have on stock market behavior.
Like a work about effect of emotions like hope, fear and worry have on increasing or decreasing
amount of Dow Jones on the next day [11] or investigating effects of Facebook [12] on stock
market. The relation between the tendencies of investors and activities of stock market found by
using a new time scale which operates on updated mood of about 100 million American
Facebook users between the periods of 10/09/2007 to 10/09/2010. In this paper, predicting of
trading volume is considered which is similar to the introduced methods.
3. IMPORTANCE OF TRADING VOLUME
Stock market is one of the first options of attracting investments and main financial indexes of
country [13]. One of the most important parameters affecting the dynamics of the stock market is
its trading volume. Stock trading volume includes the number of lots bought and sold which is
expressing in daily basis [14]. The more trading volume of a stock is higher, the more the stock is
active. Trading volume is an approving to price patterns in technical analysis and it's more
important than stock price. If we could predict the moving direction of trading volume of a stock
in the future, we can also obtain the prices changing, continuing or finishing of its trend, with
more confidence [15].
3.1. LINEAR REGRESSION
Regression predicts a numerical value [16]. Regression performs operations on a dataset where
the target values have been defined already. And the result can be extended by adding new
information [17]. The relations which regression establishes between predictor and target values
can make a pattern. This pattern can be used on other datasets which their target values are not
known. Therefore the data needed for regression are 2 part, first section for defining model and
the other for testing model. In this section we choose linear regression for our analysis. First, we
divide the data into two parts of training and testing. Then we use the training section for starting
analysis and defining the model. Scatter plot of 80% out of data has been shown in (figure 1) with
taking this into consideration that the (Average) parameter is the mean of the prices of Open,
Low, High and close. Scatter plot has been shown with just the Average parameter in order to be
simpler.

27
Figure1. Scatter plot of trading volume
Relationship between trading volume (Volume) as the dependent variable and the average price
per share (Average) as the independent variable of the regression equation
including the R-squared ( ) that has been calculated in (table 3) and shown with a red
trend line in (figure 1). R-squared shows that the two variables were used for determining the
orientation of trend line is 35.8% related. This value is used for analysis based on scatter plot of
(figure 1). For the first step correlations or relationship between desired independent parameters
for specific the relation between stock prices according to that it is in Open, Low, High, Close
and Volume status is obtained, as shown in (table 2). Coefficients have been calculated to 3
decimal (the relations are between 80% out of the whole data).
Table2. The relationship between independent parameters
Open Close Low High
Lose 0.959 - - -
Low 0.975 0.989 - -
High 0.989 0.976 0.985 -
Volume -0.383 -0.429 -0.425 -0.391
As it is obvious from the relationship chart of table 2, the relationship of 4 values of S&P 500
indexes are close to 1, and also the independence value of the dependent variable of Volume with
other 4 prices is close to 0. By using data analysis that is one of the facilities of Excel which is
used for financial analysis and defining predicting patterns, linear regression applied to the data.
Summary output of applying the regression analysis has shown in (table 3). (Coefficients are
considered simple).
Table3. Achieved regression values by applying regression analysis
Regression Statistics
Multiple R 0.599
R Square 0.358
Adjusted R Square 0.347
Standard Error 285577
Observations 59
The value of multiple R is 0.599 or 0.6. This value is close to 1 which means that the regression
line along with least square value is appropriate and well-adjusted to data.

28
and , this values are close to 0 which means that the average and
volume points are close to the trend line shown in figure 1. Since we use linear regression and
take independent parameter of average into consideration. Therefore R square value is the value
of . The standard error is equal to 285577 which is the error between real values and
estimated value of volume has been calculated from summation of all residual values along with
degree of freedom, sum and mean of squares shown in table 4.
Table4. Analysis of variation of linear regression
Table5. Coefficients obtained from applying linear regression
Coefficients Standard Error
Intercept 4675513 697440
Average -106938 18953
Using coefficients obtained from the figure 5, correlation of linear regression obtained as:
The linear regression of trading volume = 4675513-106938 * Average
After obtaining coefficients, slope, error and intercept and applying linear regression on sample
data, for testing that how much close the formula can predict the trading volume (which is our
unknown parameter) to real volume, we applied this formula on the rest 20% of data. The results
shown in table 6 obtained (some samples of results have been presented).
Table6. Results of the applying regression formula
Date Average Price Predicted Volume Volume
28/06/2103 33.13 $965675 $1,081,200
27/06/2013 32.96 $963498 $801,800
26/06/2013 32.49 $1019301 $835,100
25/06/2013 32.34 $1042679 $1,196,700
24/06/2013 32.87 $985747 $656,100
21/06/2013 32.94 $964849 $1,017,800
20/06/2013 33.11 $955342 $1,196,100
18/06/2013 33.53 $921192 $1,156,600
17/06/2013 33.52 $919738 $1,794,100
14/06/2013 33.52 $918908 $2,512,100
07/06/2013 35.88 $758848 $645,000
ANOVA df SS MS
Regression 1 3E+12 3E+12
Residual 57 5E+12 8E+10
Total 58 7E+12

29
As it’s obvious from table 6, the predicted trading volume is very similar to real values. By
computing the difference between real and predicted values of proposed approach shown in
figure 6, similarities of 61.35% observed
5. DISCUSSION
Financial markets such as stock market are generating constantly great volume of information
needed to analysis and to produce any predicting pattern in any time. Therefore they are
interesting case of using different scientific methods to development and improvement in
generating techniques. Each of the used techniques for predicting financial matters has some
benefits and limitations of its own which causes to some weakened or strengthened status. With
taking this matter into consideration that our study is a case study on S&P 500 index to compare
with other techniques, we checked out 8 most important features for predicting methods. The first
feature is ease of encoding, which our method is equal to rule induction and has high degree in it
and it is better than ANNs and genetic algorithm.
Second feature is accessibility or availability of off-the-shelf software that for this feature it is
equal to rule induction, statistical inference and ANN and has high degree in it. Third feature is
flexibility or ability of covering different types of large scales is equal to statistical inference and
genetic algorithm and has medium degree in it. Fourth feature is autonomy or independence of
prior assumptions from relations between variables and domain theories is equal to rule induction
and statistical inference and is weak in this feature.
Fifth feature is optimization capability which tries to generate optimized results, in this feature is
equal to genetic algorithms and has medium efficiency in it. Sixth and seventh features are
operative complexity and cost of calculation in generating the results which has medium degree
in them. In the case of eighth feature which is interpretability or ability of explaining results has
high degree like rule induction and data visualization [18].
7. CONCLUSIONS
Each clustering algorithms are solely capable of focusing on particular parts of customers' data in
electronic shops. This focus brings better and more detailed results to the same parts. Meanwhile,
in analysing other parts, due to the lack of clustering analyses, it brings challenges to them.
So, each algorithm is capable of doing detailed analyses of some parts of customers' data. To
provide comprehensive results and clustering analyses, it must be used several integrated and
clustering algorithms. We, in this paper, investigate different types of methods and clustering
algorithms. Finally, by using K-means, farthest first, EM samples of customers of an E-commerce
websites, we made clustering vie Weka software.
We indicated that each algorithm covers the clustering analyses weaknesses of other algorithms
for some customers. The integrated data of all algorithms analyses brings detailed results from
customers' behavioural method and its relation with shopping basket as well. So, by using
integrated collective data, it can be determined marketing policies and customer satisfaction
appropriate to all customers' clustering and their orientation which finally lead to increased
productivity and incomes.

30
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Authors
Farhad Soleimanian Gharehchopogh is currently Ph.D. candidate in
department of computer engineering at Hacettepe University, Ankara, Turkey.
And he works an honour lecture in computer engineering department, science
and research and Urmia branches, Islamic Azad University, West Azerbaijan,
Iran. He is a member of editorial board and review board in many international
journals and international Conferences. His interested research areas are in the
Operating Systems, Software Cost Estimation, Data Mining and Machine
Learning techniques and Natural Language Processing. For more information
please visit www.soleimanian.net
Tahmineh Haddadi Bonab is a M.Sc. student in Computer Engineering
Department, Science and Research Branch, Islamic Azad University, West
Azerbaijan, Iran. Her interested research areas are Meta Heuristic Algorithms,
Data Mining and Machine learning Techniques.
Seyyed Reza Khaze is a Lecturer and Member of the Research Committee of
the Department of Computer Engineering, Dehdasht Branch, Islamic Azad
University, Iran. He is a Member of Editorial Board and Review Board in
Several International Journals and National Conferences. His interested
research areas are in the Software Cost Estimation, Machine learning, Data
Mining, Optimization and Artificial Intelligence.

A LINEAR REGRESSION APPROACH TO PREDICTION OF STOCK MARKET TRADING VOLUME: A CASE STUDY

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