Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання
A set of models of feedforward neural networks is created to obtain operational forecasts of the time series of the hryvnia/dollar exchange rate. It is shown that using an evolutionary algorithm for the total search of basic characteristics and a genetic algorithm for searching the values of the mat...
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| author | Fedin, Serhii |
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{
"author": "Serhii Fedin",
"institution": "National Transport University, Kyiv"
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| description | A set of models of feedforward neural networks is created to obtain operational forecasts of the time series of the hryvnia/dollar exchange rate. It is shown that using an evolutionary algorithm for the total search of basic characteristics and a genetic algorithm for searching the values of the matrix of neural network weight coefficients allows optimizing the configuration and selecting the best neural network models according to various criteria of their training and testing quality. Based on the verification of forecasting results, it is established that the use of neural network models selected by the evolutionary modelling method increases the accuracy of forecasting the hryvnia/dollar exchange rate compared to neural network models created without the use of a genetic algorithm. The accuracy of the forecasting results is confirmed by the method of inverse verification using data from different retrospective periods of the time series using the criterion of the average absolute percentage error of the forecast. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2024.3.01 |
| first_indexed | 2025-07-17T10:28:34Z |
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Publisher IASA at the Igor Sikorsky Kyiv Polytechnic Institute, 2024
Системні дослідження та інформаційні технології, 2024, № 3 7
TIДC
МЕТОДИ, МОДЕЛІ ТА ТЕХНОЛОГІЇ ШТУЧНОГО
ІНТЕЛЕКТУ В СИСТЕМНОМУ АНАЛІЗІ
ТА УПРАВЛІННІ
UDC 004.8:336
DOI: 10.20535/SRIT.2308-8893.2024.3.01
IMPROVING THE ACCURACY OF NEURAL NETWORK
EXCHANGE RATE FORECASTING USING EVOLUTIONARY
MODELING METHODS
S.S. FEDIN
Abstract. A set of models of feedforward neural networks is created to obtain op-
erational forecasts of the time series of the hryvnia/dollar exchange rate. It is shown
that using an evolutionary algorithm for the total search of basic characteristics and
a genetic algorithm for searching the values of the matrix of neural network weight
coefficients allows optimizing the configuration and selecting the best neural net-
work models according to various criteria of their training and testing quality. Based
on the verification of forecasting results, it is established that the use of neural net-
work models selected by the evolutionary modelling method increases the accuracy
of forecasting the hryvnia/dollar exchange rate compared to neural network models
created without the use of a genetic algorithm. The accuracy of the forecasting re-
sults is confirmed by the method of inverse verification using data from different
retrospective periods of the time series using the criterion of the average absolute
percentage error of the forecast.
Keywords: exchange rate, genetic algorithm, evolutionary modeling, neural net-
work, optimization, forecasting, accuracy, time series.
INTRODUCTION
In the foreign and domestic practice of financial analysis and forecasting, artifi-
cial intelligence information technologies are widely used, which are currently an
integral auxiliary tool in the process of making managerial decisions in the field
of economics and finance [1]. The use of these technologies, in particular, con-
tributes to the successful solution of the tasks of forecasting currency and stock
exchange rates, assessing the risk of financial and banking operations, analyzing
and forecasting market indicators, credit ratings of businesses etc. [1–3].
Management of economic entities, including financial systems, is carried out
under conditions of uncertainty, which necessitates the use of methods of obtain-
ing information on economic indicators to make a reasonable judgment about
possible future states of the system or alternative ways and timing of their imple-
mentation. Future uncertainty cannot be completely eliminated, so the main task
of decision-making under uncertainty is to find “good” or “best” decisions from a
range of alternatives.
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 8
One of the tools in the process of making such decisions is the forecasting
methodology [4; 5]. The need to use different forecasting methods is caused by
the fact that in the context of nonlinear dynamic processes of financial markets,
determining their future states is a difficult task, but obtaining reliable informa-
tion about the value of financial indicators is a key aspect of supporting decision-
making at a certain point in time.
According to the results of independent studies confirms the assumption that
the time series of financial indicators, in particular, stock prices and exchange
rates, are characterized by nonlinear trends at different periods of retrospection
[6–9]. The dynamics of exchange rates is characterized by complex nonlinear de-
pendencies with a high level of noise and veiled periodic components with vari-
able amplitude, which causes the presence of heterogeneous components in the
time series and does not allow for the selection of a single model structure for the
entire time series data set [10]. Thus, at different periods of retrospection, the
structure of the model (the nature of the trend) changes, this increases the degree
of information uncertainty and reduces the reliability of forecasting. The solution
to this problem requires the use of artificial intelligence methods, including neural
networks and evolutionary modeling.
A common characteristic of these non-parametric information processing
methods is the ability to recognize patterns — trends based on the generalization
of input information [11]. The ability to model nonlinear processes and adaptabil-
ity allow the use of neural networks and evolutionary algorithms in solving vari-
ous forecasting problems in the face of noisy input data [12; 13]. In addition,
compared to classical analytical models, neural networks allow obtaining reliable
forecast estimates for non-stationary and periodic time series of financial indica-
tors [11].
Thus, the use of neural network and evolutionary forecasting methods can be
viewed as a generalization of traditional approaches to solving the urgent problem
of recognizing trends in the time series of exchange rates and timely management
decision-making.
PROBLEM DEFINITION
To build a multilayer feedforward neural network, let us assume that the set of
training sample examples is represented by data vectors (X, Y), the structure of
which determines the number of inputs N and outputs M of the neural network, where
),,,( 21 NxxxX is the value of the input vector, and ),,,( 21 MyyyY —
the desired (actual or reference) values of the output vector.
Then the process of training a neural network as a dynamic system consists
in achieving such a state of the network in which the differences between all out-
put Y and the desired values of the training sample vectors Y do not exceed the
value of the error , which is determined in advance and calculated in a certain
way. In this case, the task of training a neural network is to determine the values
of all its characteristics, so that when any vector X from the set of training ex-
amples ),( YX is fed to the input, the neural network output for a given set of
weight coefficients W is the vector )}(,),(),({)( 21 WyWyWyWY M , which
differs from the reference vector Y by no more than value of error .
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 9
In this case, the objective function (training criterion) will be the error
)(max W — the maximum difference between Y and Y for all vectors of the
training set containing n elements. The minimum value of the error will allow
obtaining the maximum training accuracy of the neural network model.
The objective function is represented as the sum of the squares of deviations
of the values Y from the values Y , obtained by the dynamic process of propaga-
tion of training sample examples from the inputs to the outputs of the neural network
M
k
kki WYYWYYW
1
22
))((
2
1
)(
2
1
)( . (1)
Then the iterative process of finding the weights of inter-neuronal connec-
tions W of the neural network that would satisfy the given value of criterion (1)
can be carried out by the gradient descent method based on the dependence
))((grad)()1( nWnWnW W , (2)
where is the step size (error correction rate coefficient).
To obtain an estimate of the learning criterion (1) and find the vector weights
of the neural network (2), the Back Propagation of Error algorithm can be used.
The disadvantage of this algorithm is that it can only find local minimum of the
objective function (1). Since the task of finding the characteristics of a neural
network that satisfies the condition 0)( max W for real data is unattainable and
is usually not set, the optimal solution turns into the search for a better or rational
solution [14]. An effective way to find such a solution is to use the mathematical
apparatus of genetic algorithms, the functioning of which is based on the mecha-
nisms of natural evolution using selection and crossover operators of parental in-
dividuals, mutation of offspring and assessment of their fitness [12; 15–17]. Since
all of these operators are collectively aimed at improving each individual, the pre-
liminary results of the genetic algorithm will be iterative improvements in the so-
lution population compared to the initial population, the size of which remains
constant. The resulting neural network individual differs from its parent(s) and
may be more or less adapted to transmit genetic information (chromosomes) to
subsequent generations, which is characterized by an estimate of the fitness func-
tion. The chromosome of an individual consists of neurons — genes, each of
which is represented by a set of values of its input weights [16; 18].
Let us represent individuals as a vector containing meaningful “genetic” in-
formation in the form of input and output weights of the neural network
) , ,( out
j
hidinp WWWW , where inpW — is the vector of input weights of the
neural network; j
hidW — is the vector of weights between the j-th and (j+1)-th
hidden layers of a multilayer neural network; outW — is the vector of output
weights of a neural network; 1...1 kj , where k is the number of hidden layers.
The dimension of W is equal to MJJJJJJN kkk 1211 ...)1( , where jJ
is the number of neurons in the j-th hidden layer [19].
Then, the task of building a complete neural network can be solved in two
stages, each of which requires the use of a specific genetic algorithm, namely:
– a total search for the basic characteristics of the neural network topology,
i.e. determining the number of hidden layers k and neurons in each hidden layer J
(Fig. 1);
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 10
– optimization of the neural network configuration by determining the “best”
combination of the values of the weight coefficients W of all inter-neuronal con-
nections (Fig. 2).
RMS Error;
Average Error;
Sum of R-Squared;
Number Good;
Number of Runs.
Genotype →
→ Phenotype
Yes
The initial population of chromosomes
Chromosome decoding
Many new unknown models
neural networks
Training neural network models
(Back Propagation of Error)
A set of trained neural networks
Has the completion
condition been met?
No
The beginning
Creating neural
networks
Testing neural networks
Evaluation of neural networks
The value of the fitness function of each
chromosome in the population
The end
The “best” neural
network architecture
Selection
of chromosomes
Application of genetic
operators
Creation
of a new population
Fig. 1. Flowchart of the genetic algorithm for finding the neural network
topology — evolution of architectures
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 11
Let us present four fitness functions (Table 1) for their sequential application
in the genetic algorithm for optimizing the configuration of a neural network
model (Fig. 2).
In accordance with the value of one of the selected fitness functions (Table 1),
the genetic algorithm (Fig. 2) allows iteratively improving the population of
neural network individuals and determining the neural network configuration
that corresponds to the minimum error value (1), which can ultimately con-
tribute to improving the accuracy of operational forecasting of time series of
exchange rates.
Fitness functions:
Number of facts within
tolerance of;
Minimum average error;
Minimum squared error;
Maximum sum of
R-squared error.
Genotype →
→ Phenotype
Yes
The initial population of chromosomes
Chromosome decoding
Multiple models
neural networks with specified
weight coefficients
Calculation of the absolute RMS error
between the actual and the set value at the
outputs of neural networks based on training
standards fed to each neural network
Has the completion
condition been met?
No
The beginning
The value of the fitness function of each
chromosome in the population
The end
The “best” combination of
neural network weights
Selection
of chromosomes
Application of genetic
operators
Creation
of a new population
Fig. 2. Flowchart of the genetic algorithm for finding the weighting matrix of a neural
network — evolution of weights
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 12
T a b l e 1 . Types of fitness functions for the genetic algorithm for finding the
matrix of neural network weighting coefficients (evolution of weights)
Criterion Type of fitness function
Number of facts
within the
tolerance of
)( minmax YYTOLYY ,
where TOL is the accuracy parameter of neural network
training and testing
(3)
Minimum
average error
)1(max Avg Error ,
where
n
i
ii YY
n
Avg Error
1
1 .
(4)
Minimum
squared error
)1(max RMS Error ,
where
n
i
ii YY
n
RMS Error
1
2)(
1
(5)
Maximum sum
of R-squared
error
)(max 2 R ,
where
2
11
2
2
11
2
2
1 1 12
)(
n
i
i
n
i
i
n
i
i
n
i
i
n
i
n
i
n
i
iiii
YYnYYn
YYYYn
R .
(6)
RESEARCH OBJECTIVE
This study is dedicated to improve the accuracy of neural network forecasting of
the exchange rate of the currency pair hryvnia/dollar through the use of a genetic
algorithm that allows to optimizing the configuration and perform an evolutionary
search for the best neural networks models according to a given criterion of the
quality of their training and testing.
LITERATURE REVIEW
The studies of S.A. Ayvazyan, I.G. Lukyanenko, L.I. Krasnikova, P.I. Bidyuk,
O.V. Polovtsev, I.V. Baklan, V.M. Rifa, J. Johnston, J. DiNardo, G.E.P. Box,
G.M. Jenkins demonstrate that the use of time series analysis methods is one of
the most common approaches to forecasting the development of economic sys-
tems and processes, evaluating alternative economic strategies, as well as manag-
ing economic and financial risks [20–26].
It is known that the purpose of time series analysis is to obtain useful infor-
mation from an ordered sequence of real numbers tx , Tt ,,2,1 , which are
the results of observations of a certain value, based on a certain mathematical
model [11; 27]. Such a model should explain the essence of the dynamic process,
in particular, describe the nature of the data, which can be random, stationary,
non-stationary, or periodic [27]. Time series of currency exchange rates or stock
price movements usually contain random fluctuations and noise in varying pro-
portions [11]. Therefore, the quality of the model is largely determined by its abil-
ity to approximate the regular (predictable) structure of the time series, separating
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 13
it from the noise. To solve this problem, methods of statistical analysis of time
series are effective, including linear autoregressive moving average models
(ARMA), ARMA+trend models, and methods of forecasting nonlinear processes,
which include artificial neural networks [9]. The peculiarity of using neural net-
work models is the ability to reproduce any dependence of the form
tptttt xxxfx ε) ..., ,,(ˆ 21 with a continuous function f based on the delay
vector between current and past data ),,,( 21 pttt xxx in n-dimensional space
of time-shifted values [11; 19].
However, under conditions of uncertainty of the future situation, associated,
for example, with changes in the nature of the trend of financial indicators at dif-
ferent time intervals, the task of fully building a neural network model is complex
both in terms of its dimensionality and in terms of ensuring the accuracy of the
model during training and testing. One of the effective ways to solve this problem
is to combine neural networks and genetic algorithms to find the best solution
from a number of alternatives in the argument search space and determine the ex-
tremum of the objective function of the learning error (1) [12; 14]. This combina-
tion can be auxiliary when (methods are applied sequentially one after the other)
or equal (simultaneous application of both methods, for example, to find the
weights of inter-neural connections) [28; 29].
It is assumed that in the face of changing trends in financial indicators, the
use of the principle of equal combination of a genetic algorithm and a feedfor-
ward neural network will optimize the machine learning process and, as a result,
improve the accuracy of approximating the regular component of the exchange
rate time series in the selected observation interval.
Thus, conducting a study aimed at ensuring the accuracy of neural network
forecasting of non-stationary time series by using genetic algorithms in optimiz-
ing the training process of multilayer neural networks is an urgent scientific and
practical task.
MATERIALS AND METHODS
As the initial data for creating neural network forecasting models, we used factual
data of the time series of the official hryvnia exchange rate against the US dollar,
which were borrowed from the government electronic resource [30]. To assess the
accuracy of the forecast, the principle of simulation forecasting was applied, since
the actual value of the hryvnia exchange rate in relation to the one-day forecast
advance period, i.e. Tuesday 06.10.2020, is known and amounts to 28.4009 hryv-
nia per 1 dollar. In determining the dimension of the neural network training sam-
ple, we used the methods of spectral and autocorrelation analysis of time series
data, as well as the method of a branched delay line, according to which the archi-
tecture of the feedforward neural network allows us to model any finite time de-
pendence of the following form [11]
)]( ,...,)1( ,)([)( ptXtXtXFtY . (7)
The spectral analysis shows that the frequency of the first harmonic is
approximately zero (Fig. 3, a). This indicates the absence of periodicity in the
regular component of the time series, and, as a result, the appropriateness of
setting the forecast advance period to correspond to the daily change in the
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 14
hryvnia/dollar exchange rate. The result of the autocorrelation analysis (Fig. 3, b)
characterizes the non-stationary of the hryvnia exchange rate time series, since the
maximum value of the autocorrelation coefficient corresponds to the first lag
(time series shift), so the use of feedforward neural networks is an appropriate
way to obtain an operational simulation forecast. The observation period, which is
one week and corresponds to the number of inputs of the neural network training
sample, was determined taking into account the lag for which the autocorrelation
coefficient exceeds 0.85 (Fig. 3, b) [31].
Thus, in accordance with (7) and based on the obtained estimates of the time
series autocorrelation coefficients (Fig. 3, b), the training set of 274n examples
has a dimension consisting of seven inputs (Input) USD1 )7( t , USD2
)6( t ,...,USD7 )1( t and one output (Pattern) USD8 (t). Testing of the
USD_11.net neural network model with the 7:10:1 architecture, trained in the
BrainMaker Professional system for 67 epochs of training (Run), showed that all
27 facts of the test sample (10% of the number of examples of the training sam-
Fig. 3. Results of spectral analysis of the time series in NetMaker (a); autocorrelation
analysis of the time series in STATISTICA 10 (b)
a
b
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 15
ple) are classified as Good, i.e., within the tolerance range when condition (3) is
met for the value of the TOL parameter 10.0 [31]. The result of the simulation
neural network forecasting was obtained using a training example that character-
izes the last week of the observation period before Tuesday 06.10.2020 (t), i.e. the
value of the hryvnia exchange rate from 29.09.2020 )7( t to 05.10.2020 )1( t .
To ensure the convergence of the results of neural network forecasting, training
and testing of models with the 7:10:1 architecture was repeated 5L times with
the value of the TOL parameter 10.0 . The evaluation of the results of testing
neural network models (Table 2) and the accuracy of the simulation forecast for
Tuesday 06.10.2020 (Table 3) was carried out according to the criterion of the
mean absolute percentage error (MAPE)
n
i i
ii
Y
YY
n
MAPE
1
100 , (8)
where YY , are respectively the predicted (Out) and actual (Ptn) values of the
i-th example selected for testing, ni ,,1 .
T a b l e 2 . The value of the MAPE criterion, %, based on the results of testing
USD neural network models created in BrainMaker Professional
USD_11.net USD_12.net USD_13.net USD_14.net USD_15.net
0.784 0.761 0.822 0.726 0.664
The analysis of the data presented in Table 2 shows that for the test sample,
the value of the MAPE criterion is in the range (0.664...0.822%), and the lowest
value of this criterion corresponds to the USD_15.net neural network model
(Table 3).
T a b l e 3 . Evaluation of the accuracy of forecasting results using neural net-
work models created in BrainMaker Professional
Model Run Good Result MAPE, %
USD_11.net 67 27 27.875 1.85
USD_12.net 129 27 27.912 1.72
USD_13.net 83 27 27.888 1.81
USD_14.net 98 27 27.878 1.84
USD_15.net 62 27 27.883 1.82
The analysis of the data presented in Table 3 shows a high speed of neural
network training (Run parameter) and finding all the facts of the test sample with-
in the training tolerance (Good parameter) in accordance with condition (3). At
the same time, the interval of the MAPE criterion is (1.72...1.85%), the lowest
value of which corresponds to the USD_12.net model.
Attempts to create neural network models with a further reduction of the
training tolerance allowed us to establish that for a sample of initial data when the
value of the TOL parameter is set to 0.06, the machine learning process using the
Back Propagation of Error algorithm in the BrainMaker Professional system does
not converge. Therefore, the task of improving the accuracy of neural network
forecasting of the hryvnia/dollar exchange rate was solved by evolutionary mod-
eling in the Genetic Training Option (GTO) software using genetic algorithms
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 16
(Figs. 1, 2) and a smaller training tolerance compared to the models presented in
Table 3. At the same time, the assumption of increasing the accuracy of neural
network forecasting can be confirmed by fulfilling the following condition
ll MAPEMAPE
LL
USDGTO minmax , (9)
where is the l-th model of a neural network created with (GTOl) and without
(USDl) genetic algorithm, Ll ,,1 .
CONDUCTING COMPUTATIONAL EXPERIMENTS USING EVOLUTIONARY
MODELING METHODS
The experimental studies were devoted to confirming the assumption that it is
possible to improve the accuracy of neural network forecasting by using evolu-
tionary modeling methods. Computational experiments were carried out accord-
ing to a methodology that includes two stages, namely:
1) use of genetic algorithms in GTO (Figs. 1, 2) for the neural network mod-
el formed in BrainMaker Professional with randomly selected weights;
2) using the BrainMaker Professional system to automatically complete the
machine learning process.
The use of the total search algorithm in GTO (Fig. 1) with a change in the
TOL parameter and a given range of the number of neurons in the hidden layer of
the neural network allowed us to obtain the result of training the neural network
population (Fig. 4) and the model of the neural network GTO.net, all the facts of
the test sample of which, according to condition (3), are within the training
tolerance Good .27
Fig. 4. The result of GTO at the stage of total search for the basic characteristics of the
neural network when ordering the population of models by the criterion of the number of
neurons of the hidden layer Hidden 1
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 17
The main purpose of the GTO.net model, whose training was completed at
the minimum value of the TOL parameter=0.056≤0.060, is to be used to perform
crossover and mutation operators using the two best models that form the initial
population of neural networks (Fig. 4). In the process of implementing genetic
operators, in particular, it was assumed that each neural network would be trained
for 100 epochs (Run) and 30 generations would be changed. To evaluate the neu-
ral network’s adaptability, we used the results of both training and testing of the
already trained neural network model. At the same time, 50% of all neurons were
subjected to crossover and 10% to mutation. It was also assumed that the neurons
were directly crossed by 50% and 25% using a uniform and normal random vari-
able distribution law, respectively. The mutation of neurons was carried out in the
same proportion as when performing the crossover operator. The fitness (quality)
of the neural network model was assessed by one of the four GTO statistical crite-
ria (Table 1).
The result of evaluating the quality of training for the 30 formed neural net-
works according to criterion (5), ordered from the highest to the lowest value,
showed that the neural network model corresponding to the value
9735.0)1(max RMS Error is the “best”. The application of the created neu-
ral network model allowed us to obtain the forecast value of the exchange rate for
Tuesday 06.10.20, which is equal to 28.071 hryvnias per 1 dollar. The final result
of the genetic algorithm is the automatic saving of the five best out of 30 neural
network models GTO001.net, GTO002.net, GTO003.net, GTO004.net,
GTO005.net with a TOL value of 0.056. Evaluation of the results of testing the
models created using the genetic algorithm and the accuracy of neural network
forecasting according to criterion (8) is presented in Table 4 and Table 5, respectively.
T a b l e 4 . The value of the MAPE criterion, %, based on the results of testing
USD neural network models created in GTO
GTO001.net GTO002.net GTO003.net GTO004.net GTO005.net
0.349 0.348 0.369 0.357 0.388
The analysis of the data presented in Table 4 shows that for the test sample,
the value of the MAPE criterion is in the range (0.348...0.388%), and the lowest
value of this criterion corresponds to the GTO002.net neural network model.
Thus, based on a comparison of the results in Table 2 and Table 4, condition (9) is
proved to be met.
T a b l e 5 . Evaluation of the accuracy of forecasting results using neural net-
work models created by evolutionary modeling methods using GTO software and
BrainMaker Professional system
Model Run Good Result MAPE, %
GTO001.net 100 27 28.071 1.16
GTO002.net 100 27 28.075 1.15
GTO003.net 100 27 28.077 1.14
GTO004.net 100 27 28.063 1.19
GTO005.net 100 27 28.082 1.12
The analysis of the data presented in Table 5 shows that at the same speed of
the neural network model training process (Run 100 ), all the facts of the test
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 18
sample in accordance with condition (3) are within the training tolerance
(Good )27 . At the same time, the result of the evaluation of criterion (8) is in
the interval (1.12...1.15%), the lowest value of which corresponds to the
GTO005.net neural network model.
Comparison of the results in Table 3 and Table 5 shows that the accuracy of
the point forecast of the hryvnia exchange rate obtained using neural network
models created by evolutionary modeling methods is higher than that of models
created without the use of a genetic algorithm. To exclude the possibility of
obtaining a random result of neural network forecasting using evolutionary
modeling methods and to confirm the convergence of the neural network training
and testing process, computational experiments in GTO were repeated five times
using different statistical criteria: RMS Error; Average Error; Sum of R-Squared;
Number Good; Number of Runs (Fig. 1).
Thus, at the first stage of applying the GTO evolutionary algorithm to find
the basic characteristics and obtain the initial population of neural networks, in
addition to the result with a different number of neurons in one hidden layer
(Fig. 4), we obtained five more variants of ordering the initial population of
neural network individuals. Thus, given the Hidden 1 ordering criterion, the total
number of computational experiments was six. At the second stage, for the obtained
six variants of the initial population of neural networks and four criteria (3)–(6), we
repeated computational experiments to assess the adaptability of neural network
models when optimizing their configuration using a genetic algorithm (Fig. 2).
RESULTS OF COMPUTATIONAL EXPERIMENTS
An assessment of the accuracy of the results of the daily forecasting of the hryv-
nia/dollar exchange rate for Tuesday 06.10.2020, obtained on the basis of neural
network models created using a genetic algorithm, is presented in Tables 6–9 and
Figs. 5–8.
T a b l e 6 . MAPE values, % for neural network models created on the basis of
the criterion Number of facts within tolerance of
Model
Ordering criterion
GTO001 GTO002 GTO003 GTO004 GTO005
Hidden 1 1.34 1.24 1.20 1.14 1.11
RMS Error 1.34 1.12 1.15 1.25 1.18
Average Error 1.19 1.25 1.28 1.28 1.24
Sum of R-Squared 1.34 1.12 1.16 1.14 1.23
Number Good 1.19 1.32 1.21 1.22 1.15
Number of Runs 1.19 1.15 1.26 1.17 1.14
T a b l e 7 . MAPE values, % for neural network models created on the basis of
the criterion Minimum average error
Model
Ordering criterion
GTO001 GTO002 GTO003 GTO004 GTO005
Hidden 1 1.24 1.19 1.19 1.23 1.26
RMS Error 1.23 1.22 1.26 1.23 1.26
Average Error 1.22 1.26 1.16 1.23 1.14
Sum of R-Squared 1.28 1.19 1.16 1.25 1.15
Number Good 1.17 1.13 1.31 1.25 1.28
Number of Runs 1.26 1.24 1.27 1.26 1.22
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 19
T a b l e 8 . MAPE values, % for neural network models created on the basis of
the criterion Minimum squared error
Model
Ordering criterion
GTO001 GTO002 GTO003 GTO004 GTO005
Hidden 1 1.16 1.15 1.14 1.19 1.12
RMS Error 1.20 1.25 1.28 1.24 1.27
Average Error 1.20 1.15 1.22 1.27 1.18
Sum of R-Squared 1.22 1.18 1.24 1.17 1.12
Number Good 1.20 1.16 1.26 1.15 1.20
Number of Runs 1.13 1.17 1.18 1.17 1.15
1,00
1,10
1,20
1,30
1,40
1,50
1,60
1,70
1,80
1,90
2,00
GTO001 GTO002 GTO003 GTO004 GTO005
USD_11 USD_12 USD_13 USD_14 USD_15
Models
PE, %.
Sum of
R-Squared
Number
of Runs
Hidden 1
RMS
Error
Average
Error
Number
Good
MAPE, %
Fig. 5. MAPE values for forecasting the hryvnia exchange rate using five USD neural net-
work models and five GTO neural network models created on the basis of the criterion
Number of facts within tolerance of
Fig. 6. MAPE values for forecasting the hryvnia exchange rate using five USD neural
network models and five GTO neural network models created on the basis of the criterion
Minimum average error
1,00
1,10
1,20
1,30
1,40
1,50
1,60
1,70
1,80
1,90
2,00
GTO001 GTO002 GTO003 GTO004 GTO005
USD_11 USD_12 USD_13 USD_14 USD_15
Models
MAPE, %.
Sum of
R-Squared
Number
of Runs
Hidden 1
RMS Error
Average
Error
Number
Good
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 20
1,00
1,10
1,20
1,30
1,40
1,50
1,60
1,70
1,80
1,90
2,00
GTO001 GTO002 GTO003 GTO004 GTO005
USD_11 USD_12 USD_13 USD_14 USD_15
Models
MAPE, %
Sum of
R-Squared
Number
of Runs
Hidden 1
RMS Error
Average
Error
Number
Good
Fig. 7. MAPE values for forecasting the hryvnia exchange rate using five USD neural
network models and five GTO neural network models created on the basis of the criterion
Minimum squared error
1,00
1,10
1,20
1,30
1,40
1,50
1,60
1,70
1,80
1,90
2,00
USD_11 USD_12 USD_13 USD_14 USD_15
Models
MAPE, %
GTO001 GTO002 GTO003 GTO004 GTO005
Sum of
R-Squared
Number
of Runs
Hidden 1
RMS Error
Average
Error
Number
Good
Fig. 8. MAPE values for forecasting the hryvnia exchange rate using five USD neural
network models and five GTO neural network models created on the basis of the criterion
Maximum sum of R-squared error
T a b l e 9 . MAPE values, % for neural network models created on the basis of
the criterion Maximum sum of R-squared error
Model
Ordering criterion
GTO001 GTO002 GTO003 GTO004 GTO005
Hidden 1 1.39 1.29 1.28 1.33 1.16
RMS Error 1.28 1.25 1.29 1.22 1.31
Average Error 1.22 1.14 1.19 1.15 1.18
Sum of R-Squared 1.29 1.26 1.36 1.28 1.27
Number Good 1.17 1.17 1.16 1.16 1.14
Number of Runs 1.34 1.07 1.19 1.39 1.12
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 21
DISCUSSION OF THE OBTAINED RESULTS
Data analysis (Tables 6–9, Figs. 5–8) shows that the intervals of MAPE values for
neural network models trained according to criteria (3)–(6) are, respectively:
(1.11…1.34%); (1.13…1.31%); (1.12…1.28%); (1.07…1.39%), and for neural net-
work models trained without the use of a genetic algorithm (1.72…1.85%) (Table 3).
Thus, on the basis of six computational experiments, the convergence of the
process of re-training, testing and selection of the best neural network models was
confirmed, and it was found that any of the 120 neural network models
)120465( created by evolutionary modelling methods can improve the ac-
curacy of the daily forecast of the hryvnia/dollar exchange rate (Figs. 6–9). Since
the smallest interval of the MAPE value (1,12…1,28%) meets the criterion (5) —
Minimum squared error (Table 8), the forecasting results with a one-week ad-
vance warning period were obtained using the best model of the GTO005.net
neural network (Table 10) for the Sum of R-Squared ordering criterion
(MAPE=1,12%, Table 8).
T a b l e 1 0 . The result of forecasting the hryvnia exchange rate using neural
network models based on the criterion Minimum squared error
Model
Ordering criterion
GTO001 GTO002 GTO003 GTO004 GTO005
Hidden 1 28.071 28.075 28.077 28.063 28.082
RMS Error 28.061 28.045 28.038 28.049 28.041
Average Error 28.060 28.074 28.053 28.040 28.066
Sum of R-Squared 28.054 28.066 28.048 28.070 28.083
Number Good 28.060 28.071 28.043 28.074 28.061
Number of Runs 28.079 28.068 28.066 28.069 28.075
The GTO005.net model (Table 10) is characterized by the lowest forecast er-
ror value 318.0|| , where || is the a posteriori value of the deviation of the
forecast value of the hryvnia/dollar exchange rate of 28.083 from the actual value
of 28.4009 hryvnia per 1 dollar. The results of the estimates for the weekly
forecast lead time obtained using the most accurate neural network model
USD_12.net (Table 3), which was created without the use of a genetic algorithm,
and the selected most accurate model GTO005.net are shown in Table 11.
T a b l e 1 1 . Evaluation of the neural network forecasting result with a warning
period of one week from 07.10.2020 to 13.10.2020
Date Hryvnia
exchange rate USD_12.net GTO005.net MAPEUSD_12 MAPEGTO005
07.10.2020 28.364 27.913 28.082 1.590 0.994
08.10.2020 28.324 27.916 28.099 1.440 0.794
09.10.2020 28.284 27.921 28.096 1.282 0.663
10.10.2020 28.284 27.925 28.079 1.268 0.723
11.10.2020 28.284 27.913 28.058 1.310 0.798
12.10.2020 28.210 27.903 28.052 1.088 0.559
13.10.2020 28.248 27.895 28.055 1.250 0.684
Taking into account all the values of the weekly forecast lead time for the
USD_12.net and GTO005.net models (Table 11), the estimated mean absolute
S.S. Fedin
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 22
percentage error (8) is 1.318% and 0.745%, respectively. Thus, for the
GTO005.net model, the MAPE estimate is approximately 1.77 times lower than
the MAPE estimate for the USD_12.net model. Thus, the analysis of the results
obtained (Table 11), as well as in the case of the daily point forecast, shows that the
accuracy of the weekly forecast of the hryvnia/dollar exchange rate has improved.
The adequacy of the results was checked, as well as the reliability and valid-
ity of the neural network forecast was assessed using the inverse verification
method on a new retrospective period of the hryvnia/dollar exchange rate time
series — from 02.10.2023 to 19.03.2024. To obtain a weekly forecasting result
based on the data of the observation period from 02.10.2023 to 12.03.2024, the
neural network was trained in the GTO system using the Sum of R-Squared order-
ing criterion at the stage of total search for its basic characteristics, and the Mini-
mum squared error criterion to select the best neural network models (5). The
evaluation of the obtained forecasting result is shown in Table 12.
T a b l e 1 2 . Evaluation of the result of neural network forecasting with a warn-
ing period of one week from 13.03.2024 to 19.03.2024
Date Hryvnia exchange rate GTO_USD.net MAPEGTO_USD
13.03.2024 38.4924 38.379 0.295
14.03.2024 38.7878 38.399 1.002
15.03.2024 38.6854 38.518 0.433
16.03.2024 38.6854 38.453 0.601
17.03.2024 38.6854 38.451 0.606
18.03.2024 38.7998 38.499 0.775
19.03.2024 38.9744 38.526 1.150
The estimate of the MAPE criterion, taking into account all values of the
weekly forecast advance period for the GTO_USD.net model (Table 12), is
0.695%, which is less than the value of 0.745% for the GTO005.net model
(Table 11). At the same time, the test of the statistical hypothesis that there is
no significant difference between GTO005MAPE and GTO_USDMAPE , which was
performed in STATISTICA 10 based on a t-test for independent variables
)05.0696.0( p , confirms the reliability of the result of improving the
accuracy of the neural network forecast (Fig. 9).
Thus, the analysis of all the results obtained for different periods of retro-
spection of the time series of the hryvnia/dollar exchange rate under the condition
of changing the nature of its trend confirms the reliability of the results obtained
and allows us to recommend the use of evolutionary modeling methods in training
and optimizing feedforward neural networks to improve the accuracy of opera-
tional neural network forecasting of time series of exchange rates.
Fig. 9. Screenshot of the result of testing the statistical hypothesis that there is no signifi-
cant difference in the MAPE estimates for the GTO005.net and GTO_USD.net models
Improving the accuracy of neural network exchange rate forecasting using evolutionary …
Системні дослідження та інформаційні технології, 2024, № 3 23
CONCLUSIONS
1. In order to obtain an operational forecast of the hryvnia/dollar exchange
rate with a one-day and one-week lead time for different observation periods in
2020 and 2024, feedforward neural network models with the Back Propagation of
Error learning algorithm were developed using the BrainMaker Professional sys-
tem and the Genetic Training Option software.
2. Computational experiments have shown that the use of a genetic algo-
rithm in training neural networks can improve the accuracy of operational fore-
casts by optimizing the configuration and carrying out an evolutionary search for
the best neural network models in accordance with a given criterion for the qual-
ity of their training and testing compared to neural network models created with-
out the use of a genetic algorithm. The validity of the obtained forecast results is
confirmed by assessing their reliability by the method of inverse verification car-
ried out for different retrospective periods of the hryvnia/dollar exchange rate us-
ing the statistical criterion MAPE.
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INFORMATION ON THE ARTICLE
Serhii S. Fedin, ORCID: 0000-0001-9732-632X, National Transport University, Ukraine,
e-mail: sergey.fedin1975@gmail.com
ПІДВИЩЕННЯ ТОЧНОСТІ НЕЙРОМЕРЕЖЕВОГО ПРОГНОЗУВАННЯ
ВАЛЮТНОГО КУРСУ МЕТОДАМИ ЕВОЛЮЦІЙНОГО МОДЕЛЮВАННЯ /
С.С. Федін
Анотація. Створено комплекс моделей прямошарових нейронних мереж для
отримання оперативних прогнозів часового ряду валютного курсу грив-
ні/долара. Показано, що використання еволюційного алгоритму тотального
пошуку базових характеристик і генетичного алгоритму пошуку значень мат-
риці вагових коефіцієнтів нейромереж дає змогу оптимізувати конфігурацію та
відібрати кращі нейромережеві моделі за різними критеріями якості їх навчан-
ня та тестування. На основі верифікації результатів прогнозування встановле-
но, що використання відібраних методом еволюційного моделювання нейро-
мережевих моделей дозволяє підвищити точність прогнозу курсу
гривні/долара порівняно з нейромережевими моделями, які були створені без
застосування генетичного алгоритму. Достовірність одержаних результатів
прогнозування підтверджено методом інверсної верифікації за даними різних
ретроспективних періодів часового ряду з використанням критерію середньої
абсолютної відсоткової похибки прогнозу.
Ключові слова: валютний курс, генетичний алгоритм, еволюційне моделю-
вання, нейронна мережа, оптимізація, прогнозування, точність, часовий ряд.
|
| id | journaliasakpiua-article-315124 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:28:34Z |
| publishDate | 2024 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/e0/0e4e5fd51b44755f10172032be5d78e0.pdf |
| spelling | journaliasakpiua-article-3151242024-11-16T18:06:34Z Improving the accuracy of neural network exchange rate forecasting using evolutionary modeling methods Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання Fedin, Serhii exchange rate genetic algorithm evolutionary modeling neural network optimization forecasting accuracy time series валютний курс генетичний алгоритм еволюційне моделювання нейронна мережа оптимізація прогнозування точність часовий ряд A set of models of feedforward neural networks is created to obtain operational forecasts of the time series of the hryvnia/dollar exchange rate. It is shown that using an evolutionary algorithm for the total search of basic characteristics and a genetic algorithm for searching the values of the matrix of neural network weight coefficients allows optimizing the configuration and selecting the best neural network models according to various criteria of their training and testing quality. Based on the verification of forecasting results, it is established that the use of neural network models selected by the evolutionary modelling method increases the accuracy of forecasting the hryvnia/dollar exchange rate compared to neural network models created without the use of a genetic algorithm. The accuracy of the forecasting results is confirmed by the method of inverse verification using data from different retrospective periods of the time series using the criterion of the average absolute percentage error of the forecast. Створено комплекс моделей прямошарових нейронних мереж для отримання оперативних прогнозів часового ряду валютного курсу гривні/долара. Показано, що використання еволюційного алгоритму тотального пошуку базових характеристик і генетичного алгоритму пошуку значень матриці вагових коефіцієнтів нейромереж дає змогу оптимізувати конфігурацію та відібрати кращі нейромережеві моделі за різними критеріями якості їх навчання та тестування. На основі верифікації результатів прогнозування встановлено, що використання відібраних методом еволюційного моделювання нейромережевих моделей дозволяє підвищити точність прогнозу курсу гривні/долара порівняно з нейромережевими моделями, які були створені без застосування генетичного алгоритму. Достовірність одержаних результатів прогнозування підтверджено методом інверсної верифікації за даними різних ретроспективних періодів часового ряду з використанням критерію середньої абсолютної відсоткової похибки прогнозу. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2024-09-28 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/315124 10.20535/SRIT.2308-8893.2024.3.01 System research and information technologies; No. 3 (2024); 7-24 Системные исследования и информационные технологии; № 3 (2024); 7-24 Системні дослідження та інформаційні технології; № 3 (2024); 7-24 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/315124/306017 |
| spellingShingle | валютний курс генетичний алгоритм еволюційне моделювання нейронна мережа оптимізація прогнозування точність часовий ряд Fedin, Serhii Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| title | Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| title_alt | Improving the accuracy of neural network exchange rate forecasting using evolutionary modeling methods |
| title_full | Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| title_fullStr | Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| title_full_unstemmed | Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| title_short | Підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| title_sort | підвищення точності нейромережевого прогнозування валютного курсу методами еволюційного моделювання |
| topic | валютний курс генетичний алгоритм еволюційне моделювання нейронна мережа оптимізація прогнозування точність часовий ряд |
| topic_facet | exchange rate genetic algorithm evolutionary modeling neural network optimization forecasting accuracy time series валютний курс генетичний алгоритм еволюційне моделювання нейронна мережа оптимізація прогнозування точність часовий ряд |
| url | https://journal.iasa.kpi.ua/article/view/315124 |
| work_keys_str_mv | AT fedinserhii improvingtheaccuracyofneuralnetworkexchangerateforecastingusingevolutionarymodelingmethods AT fedinserhii pídviŝennâtočnostínejromereževogoprognozuvannâvalûtnogokursumetodamievolûcíjnogomodelûvannâ |