Forecasting Price Movement of SOFIX Index on the Bulgarian Stock

Exchange – Sofia using an Artificial Neural Network Model

Veselin L. Shahpazov, Vladimir B. Velev and Lyubka A. Doukovska

Institute of Information and Communication Technologies, Bulgarian Academy of Sciences,

Acad. G. Bonchev str., bl. 2, 1113 Sofia, Bulgaria

veselin_georgiev@abv.bg, vladimir.velev@allianz.bg, doukovska@iit.bas.bg

Keywords: Forecasting, SOFIX Index, Artificial Neural Network, Business, Predicting Stock Prices, Supervised

Learning.

Abstract: The Bulgarian capital market is characterized by its relatively short history and its low liquidity, SOFIX is

the first index of BSE-Sofia based on the market capitalization of the included issues of common shares,

adjusted with the free-float of each of them. The authors intend to use a model implying an Artificial Neural

Network to predict the future price of the index. A neural network has the ability to extract useful

information from large sets of data, which often is required for a satisfying description of a financial time

series. Capital markets are known for their complexity and unpredictability and are best described as chaotic

systems. Artificial Neural Networks can be used to find relationship in large sets of data which have some

unknown relationship between input and output. Once that relationship is found, the neural network can be

used to compute the output for similar (but usually different) input.

1 INTRODUCTION

The Bulgarian capital market is characterized by its

relatively short history and its low liquidity,

especially in recent years. Yet the companies listed

represent different economic segments from the

heavy production industry to pharmaceuticals and

local banking. SOFIX is the best known and the first

index of BSE-Sofia, which calculation started on

October 20, 2000. SOFIX is based on the market

capitalization of the included issues of common

shares, adjusted with the free-float of each of them.

SOFIX is the most successful index calculated by

BSE-Sofia and is the first one on which structured

products are based on. The index covers the 15

issues of shares complying with the general

requirements for selection of constituent issues that

have the greatest market value of the free-float.

Artificial Neural Networks are flexible

computing frameworks and universal approximators

that can be applied to a wide range of time series

forecasting problems with a high degree of accuracy,

(Atsalakis, 2009). They are an artificial intelligence

method for modeling complex target functions. For

certain types of problems, such as learning to

interpret complex realworld sensor data, Artificial

Neural Networks are among the most effective

learning methods currently know. During the last

decade they have been widely applied to the domain

of financial time series prediction and their

importance in this field is

growing. The ability of neural networks to

closely approximate unknown functions to any

degree of desired accuracy has generated

considerable demand for Neural Network research in

Business. The attractiveness of neural network

research stems from researchers need to approximate

models within the business environment without

having a priori knowledge about the true underlying

function, (Sexton, 1998). However, despite all

advantages cited for artificial neural networks, their

performance for some real time series is not

satisfactory.

Predicting stock prices with traditional time

series analysis has proven to be difficult. An

artificial neural network may be more suitable for

the task. Primarily because no assumption about a

suitable mathematical model has to be made prior to

forecasting. Furthermore, a neural network has the

ability to extract useful information from large sets

of data, which often is required for a satisfying

description of a financial time series, (Nygren,

2004). In recent years, neural networks have

received an increasing amount of attention as a very

298

L. Shahpazov V., B. Velev V. and Doukovska L.

Forecasting Price Movement of SOFIX Index on the Bulgarian Stock Exchange â

A ¸S Soﬁa using an Artiﬁcial Neural Network Model.

DOI: 10.5220/0004776802980302

In Proceedings of the Third International Symposium on Business Modeling and Software Design (BMSD 2013), pages 298-302

ISBN: 978-989-8565-56-3

popular forecasting and data mining tool. Their

origin stems from the attempt to model the human

thought process as an algorithm which can be

efficiently run on a computer. Software is developed

to mimic this thought process. A neural network can

be used to find relationship in large sets of data

which have some unknown relationship between

input and output. Once that relationship is found, the

neural network can be used to compute the output

for similar (but usually different) input, (Choong,

2009). One of the advantages include automatic

learning of dependencies only from measured data

without any need to add further information (such as

type of dependency like with the regression). The

neural network is trained from the historical data

with the hope that it will discover hidden

dependencies and that it will be able to use them for

predicting into future.

Many authors propose the use of the Artificial

Neural Networks (ANN), a machine learning

method, to improve trading performance,

(Lawrence, 1997, Tilakaratne, 2008, Alhaj, 2011,

Khan, 2010, Montana, 1989, Skabar 2002, Tan,

2006, Maciel, 2008).

2 PROBLEM FORMULATION

The neural network that the authors intend to use for

predicting the price of Sofix index will be trained

with supervised learning. The network that will be

used will be a feed forward, multi-layer perceptron

network with very fast learning and an advanced

mechanism to prevent overfitting.

The Multi-layer

perceptron (MLP) networks trained using

backpropagation (BP) algorithm are the most

popular choice in neural network applications in

finance, (Atsalakis, 2009 and Atanasova, 2006). The

MLP networks are feed forward neural networks

with one or more hidden layers which is capable to

approximate any continuous function up to certain

accuracy just with one hidden layer (Cybenko,

1989).

The MLP consists of three types of layers. The

first layer is the input layer and corresponds to the

problem input variables with one node for each input

variable. The second layer is the hidden layer used

to capture non-linear relationships among variables.

The third layer is the output layer used to provide

predicted values.

The data used for the study is from the Bulgarian

stock exchange official website, and consists of the

following: last price, open, high, low and volume

traded, as well as five of the most commonly used

technical indicators (according to study conducted

by bigtrends.com): the 30 day moving average, 60

day moving average, 200 day moving average, the

14 day relative strength index and the 30 day relative

strength index. The training data covers a period of

two years and two months or from 04.01.2011 until

08.03.2013. We find the period appropriate because

it consists of an uptrend and a downtrend in the first

couple of months than the price of SOFIX

consolidates and in the last months of the observed

period enters into an uptrend. This we believe will

permit us to train the network in a better way and

produce results with a minimal error.

The training data is split into three parts, with the

major part of 50% of the data is treated as actual

training data, and the rest are treated as a testing data

(25%) and validation data (25%).

The software used during this study is

STATISTICA 7.0. The preferred Neural Network

structure was a three layer perceptron.

The software operates using back-propagation

and conjugate gradient descent algorithms for

training the network. The Artificial Neural Networks

implements the on-line version of back propagation;

i.e. it calculates the local gradient of each weight

with respect to each case during training. Weights

are updated once per training case.

The update formula is:

)1()( 







ijijij











(1)

where:

η - the learning rate;

δ- the local error gradient;

α- the momentum coefficient;

- the output of the i'th unit.

Thresholds are treated as weights with o

= -1. The

local error gradient calculation depends on whether

the unit into which the weights feed is in the output

layer or the hidden layers. Local gradients in output

layers are the product of the derivatives of the

network's error function and the units' activation

functions. Local gradients in hidden layers are the

weighted sum of the unit's outgoing weights and the

local gradients of the units to which these weights

connect.

The Conjugate gradient descent (Bishop, 1995;

Shepherd, 1997) is an advanced method of training

multilayer perceptron’s. It usually performs

significantly better than back propagation, and can

be used wherever back propagation can be. It is the

recommended technique for any network with a

large number of weights (more than a few hundred)

Forecasting Price Movement of SOFIX Index on the Bulgarian Stock Exchange – Sofia using an Artificial Neural Network

Model

299

and/or multiple output units. Conjugate gradient

descent is a batch update algorithm: whereas back

propagation adjusts the network weights after each

case, conjugate gradient descent works out the

average gradient of the error surface across all cases

before updating the weights once at the end of the

epoch.

The most widely used activation function for the

output layer are the sigmoid and hyperbolic

functions. In this paper, the sigmoid transfer

function is employed and is given by:







)(

(2)

The criteria which will evaluate the Neural

Networks performance will be the error of the

network on the subsets used during training (Root

Mean Square-RMS).

RMS









)

(



(3)

This is less interpretable than the performance

measure, but is the figure actually optimized by the

training algorithm (at least, for the training subset).

This is the RMS of the network errors on the

individual cases, where the individual errors are

generated by the network error function, which is

either a function of the observed and expected

output neuron activation levels (usually sum-squared

or a cross-entropy measure); or Sum-squared. The

error is the sum of the squared differences between

the target and actual output values on each output

unit. This is the standard error function used in

regression problems.

The weights and biases of the network are

automatically initialized to small random numbers

by the software.

3 STUDY RESULTS

In order to achieve better results with training the

Neural Network the authors decided to transform the

input data from values to change. Since the period of

time that the input data represents is limited to

nearly two years the index fluctuates between a

minimum value of 286.03 and a maximum value of

455.75.

The initial results showed that the networks that

utilized all eight input parameters ( last price, open,

high, low and volume traded 30 day moving

average, 60 day moving average, 200 day moving

average, the 14 day relative strength index and the

30 day relative strength index) performed

consistently much worse than the ones that isolated

some of the input parameters. The networks that

based their prognoses solely on the last price showed

the best results in terms of test error.

The tests were conducted with different network

architecture but the best result was obtained with a

three layer perceptron, consisting of 1 input (43 time

lagged steps) 7 nodes in the hidden layer and 1

output, training consisted of 100 epochs using back-

propagation and 23 epochs using the conjugate

gradient descent algorithm, the test error amounted

to 0.119279. It is important to outline that the

software stops the learning process when the

minimum error is reached, that way it prevents the

network from over-fitting.

After taking into consideration the specifics of

the Bulgarian stock market (the extremely low

traded volume, a problem that exposes the index to

manipulation which will lead to distortion of the

network results) the authors have found appropriate

to conduct moving average smoothing to the input

data commencing with 3 days smoothing

(calculating the average value of the last three days).

As seen from the results shown in Table 1 this

data manipulation managed to bring down the test

error considerably. The table shows the effects of

increasing the period that has been smoothed, the

Table 1: Results, produced with 3 to 9 days smoothing of last price data and respective network structures learning samples

and test error (RMS).

Network structure

Input-hidden-output

Learning samples

BP/CGD

Test error

RMS

3 days smoothing 1(12)-5-1 BP-100; CGD-115 0.076298

4 days smoothing 1(12)-11-1 BP-100; CGD-58 0.089827

5 days smoothing 1(25)-15-1 BP-100; CGD-48 0.067025

6 days smoothing 1(10)-5-1 BP-100; CGD-76 0.075116

7 days smoothing 1(20)-13-1 BP-100; CGD-34 0.057099

8 days smoothing 1(15)-14-1 BP-100;CGD-68 0.057903

9 days smoothing 1(15)-5-1 BP-100; CGD-67 0.064887

Third International Symposium on Business Modeling and Software Design

300

different network structures, learning samples and

most importantly the resulted test error. The error

reaches its minimum with 7 day smoothing and a

structure of the network with 1 input (20 time lagged

steps) 13 nodes in the hidden layer and 1 output,

training consisted of 100 epochs using back-

propagation and 34 epochs using the conjugate

gradient descent algorithm, the test error amounted

to 0. 057903.

Figure 1: Structure of Neural Network with 1 input (20

time lagged steps) 13 nodes in the hidden layer and 1

output.

Figures 1, 2, 3 and 4 show structure, predicted

values versus observed plot, graphic of the

predictions over the analysed period and the residual

error diagram respectively.

Figure 2: Predicted values versus observed values plot.

As we can see from Figure 4, the error tends to

increase in in the beginning and the end of the

analysed period of time. This can be explained from

an economic perspective with the fact that during

both periods the Bulgarian stock market is in a trend

situation usually characterized with higher volatility

in the prices of stocks, especially in downtrends.

This leads the authors to believe that predictive

abilities of a neural network are better suited for

markets that find themselves in a period of

consolidation.

Figure 3: Predicted change (dotted line) versus observed

change.

Figure 4: The residual error.

The Networks that were fed with the same pre-

processed data but trained with all 10 input

parameters showed worse results. In the case with

the best results (7 days smoothing) in terms of test

error, the value of RMS 0.068935, the network

structure produced by the software was 9 input (15

time lagged steps) 21 nodes in the hidden layer and

1 output, training consisted of 100 epochs using

back-propagation and 81 epochs using the conjugate

gradient descent algorithm.

Forecasting Price Movement of SOFIX Index on the Bulgarian Stock Exchange – Sofia using an Artificial Neural Network

Model

301

4 CONCLUSIONS

In this paper, the problem of predicting the price of

Bulgarian Stock Exchange’s Sofix index using

neural networks is considered. The analyzed period

is of two years and two months or from 04.01.2011

until 08.03.2013. Data used for the case consists of

the daily values of last price, open, high, low and

volume traded 30 day moving average, 60 day

moving average, 200 day moving average, the 14

day relative strength index and the 30 day relative

strength index.

The criteria which was used to evaluate the

Neural Networks performance was the error of the

network on the subsets used during training (Root

Mean Square)

The input data was preprocessed and transformed

from values into daily changes. Initial readings

showed that better results would be achieved if the

input is one compared to using all or fragments of

the initial data set.

Smoothing ranging from 3 to 9 days was

performed in order to eliminate the effects of the low

liquidity and higher volatility in the market.

Results showed that this data manipulation

managed to bring down the test error considerably.

The produced neural network was structured by 1

input (20 time lagged steps) 13 nodes in the hidden

layer and 1 output, training consisted of 100 epochs

using back-propagation and 34 epochs using the

conjugate gradient descent algorithm, the test error

amounted to 0.057903. In comparison the best

performing network using all or partial input data

managed an error of 0.068935.

The obtained result was found good but the

authors see further room for improvement of the

predicting capabilities of the model. The error

margin is still considered big and attempts to bring it

further down will be made, especially improving the

predictive capabilities for trends. The low liquidity

and high volatility environment of the Bulgarian

stock market is a challenge that could be addressed

more efficiently with similar neural networks that

have different structure and learning algorithms.

Future work will involve different input data and

data pre-processing, possibly other types of neural

networks and algorithms.

ACKNOWLEDGEMENTS

The research work reported in the paper is partly

supported by the project AComIn “Advanced

Computing for Innovation”, grant 316087, funded

by the FP7 Capacity Programme (Research Potential

of Convergence Regions) and partially supported by

the European Social Fund and Republic of Bulgaria,

Operational Programme “Development of Human

Resources” 2007-2013, Grant № BG051PO001-

3.3.06-0048.

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