Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів
In this paper, the forecasting problem of share prices at the New York Stock Exchange (NYSE) was considered and investigated. For its solution the alternative methods of computational intelligence were suggested and investigated: LSTM networks, GRU, simple recurrent neural networks (RNN) and Group M...
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| author | Zaychenko, Yuriy Hamidov, Galib Gasanov, Aydin |
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| description | In this paper, the forecasting problem of share prices at the New York Stock Exchange (NYSE) was considered and investigated. For its solution the alternative methods of computational intelligence were suggested and investigated: LSTM networks, GRU, simple recurrent neural networks (RNN) and Group Method of Data Handling (GMDH). The experimental investigations of intelligent methods for the problem of CISCO share prices were carried out and the efficiency of forecasting methods was estimated and compared. It was established that method GMDH had the best forecasting accuracy compared to other methods in the problem of share prices forecasting. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2021.2.03 |
| first_indexed | 2025-07-17T10:27:24Z |
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Yu. Zaychenko, G. Hamidov, A. Gasanov, 2021
Системні дослідження та інформаційні технології, 2021, № 2 35
TIДC
ТЕОРЕТИЧНІ ТА ПРИКЛАДНІ ПРОБЛЕМИ
ІНТЕЛЕКТУАЛЬНИХ СИСТЕМ ПІДТРИМАННЯ
ПРИЙНЯТТЯ РІШЕНЬ
UDC 519.8
DOI: 10.20535/SRIT.2308-8893.2021.2.03
INVESTIGATION OF СOMPUTATIONAL INTELLIGENCE
METHODS IN FORECASTING
PROBLEMS AT STOCK EXCHANGES
Yu. ZAYCHENKO, G. HAMIDOV, A. GASANOV
Abstract. In this paper, the forecasting problem of share prices at the New York
Stock Exchange (NYSE) was considered and investigated. For its solution the alter-
native methods of computational intelligence were suggested and investigated:
LSTM networks, GRU, simple recurrent neural networks (RNN) and Group Method
of Data Handling (GMDH). The experimental investigations of intelligent methods
for the problem of CISCO share prices were carried out and the efficiency of fore-
casting methods was estimated and compared. It was established that method
GMDH had the best forecasting accuracy compared to other methods in the problem
of share prices forecasting.
Keywords: share prices forecasting, LSTM, GRU, RNN, GMDH.
INTRODUCTION
The problem of share prices and market indicators forecasting attracts great atten-
tion from the specialists and financial managers. Traditionally for this problem
statistical methods, ARMA, ARIMA, exponential smoothing method, Kalman
filters and other methods were used.
But these methods have some drawbacks and based on assumptions which
usually don’t fulfill in practice: financial processes are non-stationary, and non-
linear by parameters, errors are correlated and may haven’t zero mean and
bounded variance.
Therefore last years for forecasting financial processes at stock exchanges
intelligent methods are widely used. One class of such methods are recurrent neu-
ral networks (RNN) [1–7]. They enable to detect hidden dependences in data and
perform long-term forecast of time series.
Now this class of RNN includes simple recurrent networks, LSTM and GRU
[1-10]. As alternative intelligent method GMDH from the other side is also
widely used for forecasting share prices at stock exchanges [11; 12] and other
financial processes. GMDH has some advantages over other forecasting methods:
1) it enables to construct structure of forecasting model using experimental sam-
ple and find analytical models; 2) it may work with short samples.
It’s interesting to compare these alternative methods at solution of practical
forecasting problems. The goal of this paper is to investigate recurrent networks
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 36
and method GMDH at forecasting of share prices, compare their efficiency and
find the best method for this class of problem.
LSTM AND GRU MODELS DESCRIPTION
Networks of Long Short Term Memory (LSTM) were developed by “LSTM”,
Hochreiter and Schmidhuber [1; 2] LSTM — is a special type of RNN, capable to
train long-term dependencies. They work well for the most problems and are con-
structed so that to exclude problems which usually occur with deep learning net-
works. LSTM enable to prevent problem of decay or explosion of gradient when
training using Back Propagation algorithm.
The architecture of LSTM is presented in the Fig. 1. It has chains type
structure consisting of sequence of modules (blocks).
LSTM has capability to add or delete information which is regulated by
special modules — gates (Fig 2). Gate consists of sigmoidal layer
( ) and operation of pointwise multiplication.
Another RNN Gated Recurrent Unit (GRU) somewhat differs
from LSTM. It integrates input and forgetting gates in one “update
gate”.
A model GRU is therefore is more simple than conventional
LSTM (see Fig. 3) and it has won popularity and wide applications
owing to this property:
X
Fig. 2. Gate
Xt–1 Xt Xt+1
ht–1 ht ht+1
A A
Fig. 1. The architecture of LSTM network
]),[,( 1 ttzt xhWz ;
)],[,( 1 ttrt xhWr ;
],[,(tanh 1 tttt xhrWh ;
])1( 1 ttttt hzhzh .
X
X X
Fig. 3. Structure of GRU
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 37
Extended LSTM with forgetting gate. The extended LSTM is also two-
layer recurrent network (Fig. 4.) Instead of hidden neuron a memory module is
used which consists of one or more cells (Fig. 5). Forgetting gate is used to pre-
vent uncontrolled increase of variable value in a memory cell.
Training of the extended LSTM with forgetting gate is performed by error
correction method (supervised learning) in combination of Back Propagation al-
gorithm (BPTT) and recurrent training in real time (RTRL).
Fig. 4. LSTM with forgetting gate
output gating hyout
output squashing h(sc)
sc= scy
+gyin
memorizing and forgetting
input gating gyin
input squashing g(netc)
yc
wout
wφ
win
yout
yφ
yin
wc
out gate
forget gate
input gate
Fig. 5. Memory cell structure
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 38
Let’s mark advantages of LSTM networks.
1. LSTM is universal approximator like BP networks. It may ensure global
approximation of non-linear mapping of input signal into output.
2. It performs high quality generalization of input data.
3. Automatically is determined number of hidden layers (one).
4. Unlike static ANN, LSTM enables to perform adaptive filtration, fore-
casting, adaptive control, parametric models identification and classification of
non-stationary signals.
5. Unlike simple RNN (ENN, JNN, NARNN і NARMANN) LSTM enable
to work with long-term non-stationary sequences (time series).
But LSTM have also the following drawbacks.
1. Training process runs more slowly than in cases of MLP, RBFNN, PNN,
Hamming RNN, Kohonen networks.
2. Automatic determination of number of neurons (memory blocks) in hid-
den layers and number of cells in each block is absent.
3. The model of training LSTM can’t be transformed to the quadratic pro-
gramming problem in convex region which has one optimal solution.
EXPERIMENTAL INVESTIGATIONS
The goal of investigations was to estimate accuracy of share prices forecasting by
LSTM networks, find the best structure of recurrent networks LSTM, GRU and
simple RNN and compare their efficiency with method of self-organization
GMDH.
As input data share prices of CISCO at the stock exchange NYSE since 2006
till 2018 were taken. In the Table 1 daily data is presented including the fields:
Open — value of open share price of current day; High — maximal daily price
value; Low — minimal daily price; Close — close price value of current day;
Volume — sell volume value. As forecasting data was taken the field “High”.
T a b l e 1 . CISCO share prices dynamics (fragment of input sample)
Date Open High Low Close Volume Name
2006-01-03 17,21 17,49 17,18 17,45 55432166 CSCO
2006-01-04 17,48 17,93 17,85 17,85 80409776 CSCO
2006-01-05 17,94 18,48 17,93 18,35 118588943 CSCO
2006-01-06 18,51 18,88 18,47 18,77 122450979 CSCO
2006-01-09 18,97 19,11 18,92 19,06 78604868 CSCO
As a training sample was taken data since 2006 till the end of 2016 year and
a test sample the data since 2017 till 2018 year was taken. Total size of the sample
was 3019 values. The flow chart of data (share prices) is presented in the Fig. 6,
where training sample is shown in blue color while test sample — in red color.
The next step of the program run is data normalization. After that the train-
ing of neural networks is performed.
At the end of software work the flow charts of real and forecasted stock
prices, error value and accuracy of the model were determined which are pre-
sented in Fig. 7–19. For LSTM were constructed and investigated 5 models. The
forecasting results and criteria values MSE, MAE and R2 score for LSTM 1-5 are
shown in the Fig. 7–11 correspondingly.
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 39
(LSTM-1 has 4 layers, each of which consists of 100 neurons, at each eve n
layer Dropout — 0,2; uneven Dropout — 0,3)
1 — Training set (Before 2017)
2 — Testset (2017 and beyond)
CISCO Stock price
40
35
30
25
20
15
2006 2008 2010 2012 2014 2016 2018
Date
1 2
Fig. 6. Flow chart of share prices of the whole sample
1 –
2 –
1
2
Fig. 7. LSTM-1
(LSTM-2 has 4 layers, each layer consists of 50 neurons and Dropout is 0,4
at all layers)
Fig. 8. LSTM-2
1 –
2 –
1
2
Time
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 40
(LSTM-3 model has 4 layers, each of which has 30 neurons and Dropout
— 0,1 at each layer)
(This model has 4 layers, each of which has 30 neurons and Dropout — 0,2
at each layer)
Fig. 9. LSTM-3
1 –
2 –
1
2
Time
Fig. 10. LSTM-4
1 –
2 –
1
2
Time
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 41
(This model has 5 layers, each of which has 50 neurons and Dropout — 0,4
at each layer)
As it follows from presented results the best one is model 5 LSTM which
consists of 5 LSTM layers, each layer has 50 neurons and each layer uses Dropout
— 0,4) and one output layer. Training time takes about 11 minutes.
At the second stage of investigations 5 different GRU models were con-
structed and investigated. The forecasting results are presented in the Fig. 12–16.
The criteria values — MSE, MAE, MAPE, R2 are also presented.
(This model has 5 layers, each of which has 50 neurons and Dropout — 0,4 at
each layer)
1 –
2 –
1
2
Fig. 12. GRU-1
1 –
2 –
1
2
Fig. 11. LSTM-5 (the best one)
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 42
(This model has 4 layers, each hash of which has 100 neurons and Dropout —
0,4 at each layer)
(This model has 5 layers, each of which has 60 neurons and Dropout — 0,2
at each layer)
1 –
2 –
1
2
Fig. 13. GRU-2
1 –
2 –
1
2
Fig. 14. GRU-3
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 43
(This model has 4 layers, each layer consists of 80 neurons and Dropout —
0,5 at each layer)
(This model has 4 layers, each of which consists of 120 neurons with Drop-
out — 0,2 at each layer)
As it follows the best one is the 5-th network which consists of 4 GRU layers
(each layer has 120 neurons with Dropout 0,2 at each layer) and one output layer.
As training algorithm was used Stochastic Gradient Descent (SGD). Training time
1 –
2 –
1
2
Fig. 15. GRU-4
1 –
2 –
1
2
Fig. 16. GRU-5
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 44
was approximately 9 minutes. For conventional recurrent neural networks (RNN)
three models were constructed, forecasting results and criteria values are pre-
sented below in the Fig. 17–19.
(This model has 4 layers, each layer has 50 neurons with Dropout — 0,15 at
each layer)
(This model has 4 layers, each layer has 100 neurons with Dropout — 0,3 at
each layer)
Fig. 17. Simple RNN-1
1 –
2 –
1
2
1 –
2 –
1
2
Fig. 18. Simple RNN-2
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 45
(This model has 4 layers, each layer has 60 neurons with Dropout — 0,2 at
each layer)
The best RNN model appeared to be the last one which consists of 4 layers
with 60 neurons and one output layer. Each layer uses Dropout — 0,2. As a train-
ing algorithm was used Adam. Training time is about 8 minutes.
At the next experiments algorithm GMDH was used. Two models were con-
structed, trained and investigated. The forecasting results and criteria values for
models are presented in the Fig. 20, 21.
(This model differs from the other by the window size was of 60 points).
1 –
2 –
1
2
Fig. 19. Simple RNN-3
Fig. 20. GMDH-1
1
1 –
2 –
2
1
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 46
The second model GMDH turned out to be better than the first one, it has the
higher accuracy and less error. The window size for this model was 30 points,
freedom choice value is 7, regularization parameter L2 — 0,5. Training time was
about 6 minutes.
In the next experiment the comparison of the best models of different classes
was performed. Firstly the error change versus number of epochs was compared
for different models. The results are presented in the Fig. 22, 23.
1 –
2 –
1
2
Fig. 21. GMDH-2
LSTM GRU
RNN
Fig. 22. MAPE value versus number of epochs for all models
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 47
In the table 2 the results of training the best models are presented.
Table 2. Forecasting results for the best models at the test sample
Methods Models
RMSE MSE MAE R2_Score MAPE Training _Time
LSTM 0,649 0,421 0,455 90,5% 1,33 11 min
GRU 0,819 0,671 0,609 84,9% 1,79 9 min
Simple RNN 0,767 0,588 0,536 86,7% 1,55 8 min
GMDH 0,0191 0,0003 0,012 96,6% 1,28 6 min
As it follows from the presented results the best one is method GMDH by all
criteria. Besides it takes the least time for training. The second one is LSTM net-
work and the worst forecasting results were shown by GRU and simple RNN.
CONCLUSIONS
In this paper investigations of different types of recurrent networks LSTM, GRU,
simple RNN and GMDH in the forecasting problem at stock exchange NYSE
were carried out.
For each class of RNN several structures were investigated and the best
structure was selected.
The forecasting efficiency and training time of different recurrent networks
and GMDH were estimated and compared.
After experimental investigations it was determined that the best forecasting
accuracy by different criteria has method GMDH, besides it took the least training
time.
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Fig. 23. Error values (MSE) dependence on epochs number for the best models
Yu. Zaychenko, G. Hamidov, A. Gasanov
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 48
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Received 21.04.2021
INFORMATION ON THE ARTICLE
Yuriy P. Zaychenko, ORCID: 0000-0001-9662-3269, Educational and Scientific
Complex “Institute for Applied System Analysis” of the National Technical
University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
zaychenkoyuri@ukr.net
Investigation of сomputational intelligence methods in forecasting problems at stock exchanges
Системні дослідження та інформаційні технології, 2021, № 2 49
Galib Hamidov, “Azershig”, Azerbaijan, e-mail: galib.hamidov@gmail.com
Aydin Gasanov, ORCID: 0000-0002-5821-0751, Dragomanov National Pedagogical
University, Ukraine, e-mail: 0677937631@ukr.net
ДОСЛІДЖЕННЯ МЕТОДІВ ОБЧИСЛЮВАЛЬНОГО ІНТЕЛЕКТУ У ПРОБЛЕМІ
ПРОГНОЗУВАННЯ НА РИНКАХ ЦІННИХ ПАПЕРІВ / Ю.П. Зайченко,
Г. Гамідов, A. Гасанов.
Анотація. Розглянуто проблему прогнозування курсів акцій на ринку
цінних паперів NYSE. Для її вирішення запропоновано та досліджено
альтернативні методи обчислювального інтелекту: мережі LSTM, графічні
рекурентні модулі (GRU), прості рекурентні мережі і метод групового ураху-
вання аргументів (МГУА). Проведено експериментальні дослідження інтелек-
туальних методів в проблемі прогнозування цін акцій і порівняльну оцінку
ефективності альтернативних методів прогнозування. З’ясовано, що метод
МГУА забезпечує найвищу точність в розглянутій проблемі прогнозування цін
акцій.
Ключові слова: прогнозування цін акцій, рекурентні мережі LSTM, GRU,
RNN, МГУА.
ИССЛЕДОВАНИЕ МЕТОДОВ ВЫЧИСЛИТЕЛЬНОГО ИНТЕЛЛЕКТА
В ПРОБЛЕМЕ ПРОГНОЗИРОВАНИЯ НА РЫНКАХ ЦЕННЫХ БУМАГ /
Ю.П. Зайченко, Г. Гамидов, A. Гасанов.
Аннотация. Рассмотрена проблема прогнозирования курсов акций на рынке
ценных бумаг NYSE. Для ее решения предложены и исследованы альтер-
нативные методы вычислительного интеллекта: сети LSTM, графические ре-
куррентные модули (GRU), простые рекуррентные сети и метод группового
учета аргументов (МГУА). Проведены экспериментальные исследования
интеллектуальных методов в проблеме прогнозирования цен акций и сравни-
тельная оценка эффективности альтернативныхметодов прогнозирования.
Установлено, что метод МГУА обеспечивает наиболее высокую точность
в рассмотренной проблеме прогнозирования цен акций.
Ключевые слова: прогнозирование цен акций, рекуррентные сети LSTM,
GRU, RNN, МГУА.
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| id | journaliasakpiua-article-239831 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:24Z |
| publishDate | 2021 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
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| spelling | journaliasakpiua-article-2398312021-09-16T11:48:22Z Investigation of computational intelligence methods in forecasting problems at stock exchanges Исследование методов вычислительного интеллекта в проблеме прогнозирования на рынках ценных бумаг Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів Zaychenko, Yuriy Hamidov, Galib Gasanov, Aydin прогнозування цін акцій рекурентні мережі LSTM GRU RNN МГУА share prices forecasting LSTM GRU RNN GMDH прогнозирование цен акций рекуррентные сети LSTM GRU RNN МГУА In this paper, the forecasting problem of share prices at the New York Stock Exchange (NYSE) was considered and investigated. For its solution the alternative methods of computational intelligence were suggested and investigated: LSTM networks, GRU, simple recurrent neural networks (RNN) and Group Method of Data Handling (GMDH). The experimental investigations of intelligent methods for the problem of CISCO share prices were carried out and the efficiency of forecasting methods was estimated and compared. It was established that method GMDH had the best forecasting accuracy compared to other methods in the problem of share prices forecasting. Рассмотрена проблема прогнозирования курсов акций на рынке ценных бумаг NYSE. Для ее решения предложены и исследованы альтернативные методы вычислительного интеллекта: сети LSTM, графические рекуррентные модули (GRU), простые рекуррентные сети и метод группового учета аргументов (МГУА). Проведены экспериментальные исследования интеллектуальных методов в проблеме прогнозирования цен акций и сравнительная оценка эффективности альтернативныхметодов прогнозирования. Установлено, что метод МГУА обеспечивает наиболее высокую точность в рассмотренной проблеме прогнозирования цен акций. Розглянуто проблему прогнозування курсів акцій на ринку цінних паперів NYSE. Для її вирішення запропоновано та досліджено альтернативні методи обчислювального інтелекту: мережі LSTM, графічні рекурентні модулі (GRU), прості рекурентні мережі і метод групового урахування аргументів (МГУА). Проведено експериментальні дослідження інтелектуальних методів в проблемі прогнозування цін акцій і порівняльну оцінку ефективності альтернативних методів прогнозування. З’ясовано, що метод МГУА забезпечує найвищу точність в розглянутій проблемі прогнозування цін акцій. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2021-09-14 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/239831 10.20535/SRIT.2308-8893.2021.2.03 System research and information technologies; No. 2 (2021); 35-49 Системные исследования и информационные технологии; № 2 (2021); 35-49 Системні дослідження та інформаційні технології; № 2 (2021); 35-49 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/239831/238234 |
| spellingShingle | прогнозування цін акцій рекурентні мережі LSTM GRU RNN МГУА Zaychenko, Yuriy Hamidov, Galib Gasanov, Aydin Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| title | Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| title_alt | Investigation of computational intelligence methods in forecasting problems at stock exchanges Исследование методов вычислительного интеллекта в проблеме прогнозирования на рынках ценных бумаг |
| title_full | Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| title_fullStr | Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| title_full_unstemmed | Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| title_short | Дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| title_sort | дослідження методів обчислювального інтелекту у проблемі прогнозування на ринках цінних паперів |
| topic | прогнозування цін акцій рекурентні мережі LSTM GRU RNN МГУА |
| topic_facet | прогнозування цін акцій рекурентні мережі LSTM GRU RNN МГУА share prices forecasting LSTM GRU RNN GMDH прогнозирование цен акций рекуррентные сети LSTM GRU RNN МГУА |
| url | https://journal.iasa.kpi.ua/article/view/239831 |
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