=Paper=
{{Paper
|id=Vol-2649/paper6
|storemode=property
|title=Selective Adaptive Model for Forecasting of Regional Development Unevenness Indexes
|pdfUrl=https://ceur-ws.org/Vol-2649/paper6.pdf
|volume=Vol-2649
|authors=Liubov Chagovets,Natalia Chernova,Tamara Klebanova,Oleksandr Dorokhov,Anastasia Didenko
}}
==Selective Adaptive Model for Forecasting of Regional Development Unevenness Indexes==
https://ceur-ws.org/Vol-2649/paper6.pdf
58
Selective Adaptive Model for Forecasting
of Regional Development Unevenness Indexes
Liubov Chagovets1[0000-0003-4064-9712], Natalia Chernova2[0000-0002-0073-8457],
Tamara Klebanova3[0000-0002-0284-9839], Oleksandr Dorokhov4 [0000-0002-0737-8714]
and Anastasia Didenko5[0000-0001-9254-0554]
1,2,3,4
Simon Kuznets Kharkiv University of Economics, 9a Nauki av., Kharkiv, 61144, Ukraine
5
Intetics Inc., 43a Nauki av., Kharkiv,61072, Ukraine
chahovets.liubov@hneu.net
natacherchum@gmail.com
t_kleb@ukr.net
aleks.dorokhov@hneu.net
didenko.anastasya2013@yandex.ua
Abstract. The article deals with the issue of unevenness and asymmetry in the
development of regions. Particular attention has been given to current ap-
proaches for assessing and forecasting the unevenness level. The paper analyzes
the possibilities of adaptive smoothing techniques for predicting multidimen-
sional objects. The advantages and disadvantages of existing methods of predic-
tive analytics for the study of unevenness and asymmetry are shown. The adap-
tive selective model for predicting the unevenness indicators of socio-economic
development of regions was developed based on the methods of multidimen-
sional objects mathematical modeling. The selective adaptive model is based on
a combination of the exponential smoothing model and the Holt model. The
suitability analysis of models for forecasting the values of unevenness level of
socio-economic development of regions was conducted. The forecast of indica-
tors was calculated using the combined method of adaptive smoothing based on
the selective model for groups of regions with high and low socio-economic
development. The forecasts were obtained for the following indicators: number
of marriages, average wage, number of households with children, number of pa-
tients with active tuberculosis, number of detected crimes, water pollution level,
retail turnover, number of mobile subscribers, import of services. Due to the
developed selective model, the quality of the forecast was significantly in-
creased. The obtained models make it possible to improve the quality of deci-
sion-making on managing regional socio-economic development.
Keywords: Region, System, Unevenness, Socio-Economic Development, Indi-
cator, Model, Estimation, Adaptive Forecasting, Management.
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
59
1 Introduction
In today's world, there are a large number of uncertainty factors that have a signifi-
cant impact on the development of regions, regional formations and countries. They
are fluctuations in the process of economic development and affect the main areas of
balanced development. It is the deep socio-economic disparity between the regions
that is closely linked to the heterogeneity and imbalance of the economic space of the
country. Therefore, retrospective and prospective detailed analysis of the heterogenei-
ty indicators of the regional economy development is relevant. The decision-making
process in managing the economic development of regions under conditions of in-
complete information should take into account the factors of unevenness and asym-
metry of territorial development.
Comprehensive mathematical modeling of the uneven socio-economic develop-
ment of the region is of scientific and practical interest and is of particular importance
for the regional policy development.
This makes it possible to ensure a balanced development of the economy of the re-
gion and the country as a whole. This is confirmed by the fact that in the practice of
regional management due to the great diversity of subjects, complexity and multifac-
eted tasks, there are significant differences regarding the unified and generally recog-
nized methodology for assessing the unevenness level of socio-economic develop-
ment of regions. All of the above made the topic of this study relevant.
2 Literature Review
The process of improving theoretical and methodological developments on the prob-
lem of estimating and forecasting the unevenness level of socio-economic develop-
ment of regions is currently underway in Ukraine. The conducted analysis of modern
scientific literature [1 – 4, 6, 7, 9 – 21, 23 – 25, 27, 28, 30, 32 – 47, 49 – 53] has
shown that the topic of socio-economic uneven development of regional systems is
one of the most discussed in the world.
Many scientists, economists and sociologists talk about the asymmetry of regional
development [14, 17, 34, 37, 38, ], the growth of uneven development of territories [2,
9, 11, 19, 51], divergence [6, 22, 25], differentiation [7, 53, 15] and imbalance [4, 13,
24, 46]. in the development of countries and regions. It should be noted that each of
these concepts is substantially related to the differences that characterize the uneven
socio-economic development. It should also be noted that some scientists distinguish
separate phases of non-uniformity - differentiation, asymmetry, polarization. As noted
in [34], the influence of some objective factors causes the inequality, then the combi-
nation of factors increases and the links between them and socio-economic processes
are complicated. This leads to an increase in differences, further exacerbating differ-
ences, reflecting a degree of division of the territory.
The emphasis in modern research has shifted towards studying the structural char-
acteristics of the economic space [15], the features of the uneven development of
territories of different hierarchical levels [1], as the increasing unevenness begins to
60
create threats to sustainable progressive development. In the paper, we will use the
definition given in [34], that the uneven socio-economic development is understood
as a type of regional development, in which there is an increase in differences be-
tween regions in terms of accumulated economic potential, the degree of population
well-being, as well as other characteristics of economic and the social sphere of the
regions.
In addition to differences in approaches to identifying regional disparities, there are
also differing views on assessing and forecasting both unevenness indicators and as-
sessing the level and status of regional development disparities. Practical interest in
issues related to the development of methods of diagnosis and assessment of irregu-
larities is growing. The analysis of the peculiarities of methodological approaches
makes it possible to conclude that in most methods the assessment is carried out on
the integral index of socio-economic development indicators. This makes it possible
to make an assessment in dynamics, which allows for comparative analysis at differ-
ent time intervals. But along with these benefits, there are a number of disadvantages:
lack of a unified system of indicators for assessing uneven regional develop-
ment of the country; taking into account a large number of indicators, on the
one hand, significantly improves the quality of the information model, but on
the other hand, leads to information overload of decision-making processes and
complicates the interpretation of the results.
systems of indicators that form an integral level of development are not always
comparable due to the inclusion of indicators specific to a particular region.
The formed system should provide the ability to conduct a comparative (back-
ground) analysis of the socio-economic development of regions over time.
the models do not take into account the possibility of adapting model parame-
ters in accordance with a change in the direction of economic development
Thus, the theoretical foundations of developing models for balanced socio-
economic development of the regions are fully reflected in scientific papers. Howev-
er, a number of issues related to modeling the socio-economic development of regions
in the context of a cyclical crisis, assessing the heterogeneity of the economic space,
identifying factors-sources of development asymmetry, were not found most fully in
modern researches.
3 Problem Formulation, Methods
The purpose of the study is to develop an adaptive selective model for predicting
indicators of uneven socio-economic development of regions based on methods of
predictive analytics and multidimensional objects modeling.
To achieve the purpose, the following tasks should be conducted:
form a basic set of models included in the adaptive selective model;
estimate the parameters and quality of models;
61
conduct a comparative analysis of the results obtained for each base model in-
dividually and the selective model as a whole;
get a forecast of the regional development unevenness Indexes according to the
resulting model.
Forecasting the state of the regions is an important component of its assessment,
which will allow to assess later the unevenness level and the directions of strategic
planning. To develop a model basis for predicting the uneven socio-economic devel-
opment of regions, the results of the study [8], were used, which suggested a concep-
tual basis for assessing and analyzing the unevenness of regional development. Ac-
cording to the complex, a system of information representative indicators of uneven
socio-economic development was proposed. The grouping of regions by the level of
socio-economic development made it possible to assess the homogeneity and sustain-
ability of the groups obtained, determine the place of each region in the initial set,
identify structural deformations within the groups. Based on the study, two groups of
regions were identified and a model for recognizing the state of uneven socio-
economic development was constructed. As a result of the analysis of the indicators
average values, regions with a high and low level of socio-economic development
were identified. The conceptual basis allowed to form an information base for the
development of a selective adaptive model for predicting the level of unevenness and
individual structural components of the unevenness indicator.
The dynamic nature of the development of financial and economic processes often
outweighs the property of inertia, so adaptive methods that take into account infor-
mation heterogeneity of data are more effective. Adaptive forecasting methods aim at
constructing models that can independently adjust parameters and take into account
the informational value of different members of the time series and give fairly accu-
rate estimates of future members of the series. And if these methods are used simulta-
neously, i.e. in combination or selectively, the quality of short-term time series fore-
casting can be improved significantly.
Let’s analyze the peculiarities of short-term adaptive forecasting methods [5, 22,
26, 29, 31]. Exponential smoothing is most commonly used to smooth time series and
obtain short-term forecasts when series’ length is rather short.
The essence of the method of exponential observation is that in the procedure of
searching for the smoothed level only values of the previous levels of a series taken
with a certain weight are used, and the weight of the observation decreases with the
distance from the time for which the smoothed value of the row level is determined.
Consider a time series of observations . The formula for calculating the
exponential mean is:
( ) ( ) (1)
where – smoothing parameter.
The value of , ̅̅̅̅̅, calculated for the moment t, can be considered as the
prediction of the value of the level at the time : , where –
predictive value of the level. The forecast for the level is the exponential mean
62
, calculated at time . Then the prediction error at time will be equal to the
formulas:
̂ , (2)
The forecast made using the exponential mean at time is equal to the forecast
made at time plus some correction that depends on the forecast error for time .
This is called the exponential mean adaptation. In essence, there is no adaptation,
since all the corrections are made with a constant coefficient [5, 23, 28]. And since
the actual value of , is unknown, and hence the error , then we have to re-
place with the mathematical expectation which is zero for any t.
The following problems arise when using the exponential smoothing method:
1. parameter choice. If it is necessary to increase the contribution of the previous
value, is chosen close to 1; if the aim is to eliminate the influence of the individ-
ual previous values of the time series, then the sufficiently small values of parame-
ter are used;
2. select the initial value of . It is usually taken to be equal to the first value of the
time series, or the arithmetic mean of several initial levels of the series.3) Expo-
nential averages are particularly poor when the series has a downward or upward
trend. In these cases, the forecasts become either too high or too low. The larger
width of the confidence interval indicates the poor adequacy of the forecast model.
All forecasts for moments greater than , will be constant and equal to
̃ . This fact is a major drawback of the exponential mean as a predictive
tool.
3. The disadvantage of the exponential mean model is the delay (shift) effect. A de-
crease in the smoothing parameter leads to shift increase and vice versa. If the time
series increases, then the shift is positive, that is, the forecasts will be below the
true values, and if the time series decreases, the shift is negative, that is, the fore-
casts will be higher than the true values.
The development of adaptive smoothing models are models that combine the ele-
ments of exponential smoothing and allow the effects of linear trends to be distin-
guished. One such model is the Holt model. Holt was the first to use two smoothing
parameters to construct forecasts using a linear model:
̂ ( )+ ( ) (3)
where ( ) – parameter that characterizes the change in the average process level;
( )– parameter that determines the variability (increment) of the process per unit
time.
When you receive more data, formulas to improve forecasts will be as follows
[22].
( )= ( ) ( ) ( ) ( ) (4)
where – first smoothing parameter.
63
In general, estimating a prediction error when using a Holt model is a very time-
consuming task. The coefficient ( ) is defined as the exponential mean for the in-
crements of the parameter ( ):
( ) ( ( )– ( – )) ( – ) ( – ), (5)
– second smoothing parameter.
As noted in [31], the lack of classical models can be eliminated by more flexible
combined forecasting models, which include several simpler adaptive models. There-
fore, it is proposed to use an adaptive selective prediction model to overcome the
shortcomings of the above models. In combined models of selective type, at each
step, automatic selection according to the given criterion of the best model from
among those included in the basic set is organized. Thus, adaptation occurs at two
levels: by structure or type of model and by parameters. In a combined hybrid model,
the forecast is formed as a weighted sum of forecasts obtained by alternative models.
The weights are adaptive.
The essence of this model is as follows. At each step, several base models define
predictive values that are compared to actual ones. Then the best performing model is
used to find new predictive values. In the next step, the procedure is repeated [31].
Thus, the forecast for τ steps is determined as follows:
̂ ̂ ( ) , τ > 0, (6)
where ̂ ( ) – model forecast number at time for steps.
The model number at time is defined as follows:
̃ (11)7
where – number of base set of models;
̃ – exponentially smoothed mean square error of the th model at time :
The basic set of adaptive selective models is formed automatically. The calcula-
tions of the future values of the series are performed for each of them individually,
but the estimated value obtained by the model that best reflects the real process at a
given time interval is selected as a forecast.
The best model is selected according to the specified selection criterion. The crite-
rion for the average absolute percentage error for a given prediction period is also
used to select the best model variant.
| ̂| | |
∑ ∑
The smaller the value of this indicator, the better the quality of the model being se-
lected, ie the theoretical values are closer to the real values of . The model is con-
sidered to provide a sufficiently high prediction accuracy if the average absolute error
(m.a.p.e.) does not exceed 10%. If (m.a.p.e.) is in the range of 10% to 20%, then one
can speak of a satisfactory forecast accuracy.
64
Switching to a specific model is carried out when its selection criterion is minimal
compared to the same indicator for the rest of the models in the base set. It should be
noted that the use of an adaptive selective model is effective when the basic models
are significantly different.
Thus, in the short-term forecasting, the dynamics of the studied indicator at the end
of the observation period is usually more important, rather than the tendency in its
average development, which has developed over the whole retrospective period.
4 Findings
In accordance with the considered concept of the study, models of prediction of input
indicators of unevenness was developed for the following groups of indicators: social,
economic and agricultural potential and security. These groups contain the following
indicators: number of marriages, number of households with children, number of
crimes detected, average monthly wage of workers, incidence of active tuberculosis,
discharge of contaminated return water into surface water bodies, retail turnover,
number of mobile subscribers, import of services, GRP per capita, capital investments
per capita, volume of industrial production per capita, profitability of operating activi-
ties of enterprises, labor productivity in agricultural enterprises [48].
Consider the forecasting of 14 indexes of regional unevenness development by the
adaptive selective model. The set of indexes was determined from the previously
research: Number of marriages, Average wage, Number of households with children,
Number of patients with active tuberculosis, Number of crimes detected, Water pollu-
tion level, Retail turnover, Mobile subscribers, Import of services [8]. Let’s consider
the forecasting of variables on the example of the average wage coefficient in Ukraine
by region. The training and forecasting set are based on the monthly data of Kharkiv
region for 2016-2017, since the considered annual data for 2010-2017 are very vola-
tile, so the sample will be 24 periods [48]. In this case, a short-term forecast of the
dynamics of the average wage in the Kharkiv region for the 1 period forward – 1
month is constructed. The coefficient values are predicted using a selective adaptive
model, which is based on a combination of the exponential smoothing model and the
Holt model. Both models are used in short-term time series forecasting. Consider the
dynamics of average wages in the Kharkiv region in dynamics (Fig. 1).
8000
6000
4000
2000
0
0 5 10 t 15 20 25
Fig. 1. Dynamics of the average wage in the Kharkiv region
65
The time series will be divided into two parts. For the first part, which is a sample
of 14 values, we construct exponential smoothing model and the Holt model. Then we
make forecasts for each model for one step ahead. Further, in order to estimate the
forecasts obtained, we compare them with the actual value on the observation, using
the average absolute percentage error as the measure of the forecast quality. Finally,
we will summarize all the results obtained in a single table. According to the results
of the forecast for the one step forward (15 period), we will select the most adequate
model. It will be the basis for building an adaptive selective model for the last 10
periods. As a result, the forecast for the25-th period will be obtained.
First step. Construction of an exponential smoothing model. We carry out expo-
nential smoothing at a = 0.9. As the initial value of the exponential mean, we take the
arithmetic mean of the levels of the series, which equals 4621.6 UAH in a sample of
14 values. The obtained model of exponential smoothing with a forecast of 1 step
forward is presented in Fig. 2.
6000
5000
4000
3000
Y Y- фактичні значення
– actual values
2000
Експоненційне згладжування
exponential smoothing
1000
0
0 5 10 15
Fig. 2. Actual and calculated values (exponential smoothing model)
According to the results we can see that the forecast value for the 15th period
equals 5481.7 UAH, that is, the model predicts a decrease in wages. Also, on this
chart, you can see the disadvantage of exponential smoothing - the shift effect pres-
ence. In shift cases, the forecasts become either too high or too low, as shown in the
graph.
The second step. The Holt model was built for a1 = 0.9 and a2 = 0.7. The initial
values of the Holt model indices are the linear trend OLS estimates. The results of the
model with the forecast for 1 period are presented in Fig. 3.
66
6000
5000
4000
3000
Y - фактичні
Y – actualзначення
values
2000
Модель
HoltХольта
model
1000
0
0 2 4 6 8 10 12 14 16
Fig. 3. Actual and calculated values (Holt model)
The quality of this forecast will be determined in the next stage of the work. In this
case, when comparing the obtained calculations with the actual values, we see that the
Holt model also has a delay effect. However, unlike the exponential smoothing mod-
el, the result on the graph is better. Let's check this assumption in the next step.
The third step. The criterion for the mean absolute percentage error (M.A.P.E.) is
used to select the best model variant. The smaller the value of this indicator, the better
the quality of the model, because the theoretical values of Yi are closer to the real
values. The model is considered to provide a fairly high prediction accuracy if
M.A.P.E. does not exceed 10 %. If M.A.P.E. is in the range of 10 % to 20 %, then we
can speak about the satisfactory accuracy of the forecast. Comparative analysis of the
calculated models has the following results (Fig. 4).
Exponential smoothing
M.A.P.E. = 0,053908 5,39 % Excellent forecast quality
Holt model
M.A.P.E. = 0,046854 4,69 % Excellent forecast quality
Fig. 4. M.A.P.E. value for forecasting models
M.A.P.E. for the exponential smoothing model at a = 0.9 is 5.39 %, for the Holt mod-
el at a1 = 0.9 and a2 = 0.7 equals 4.69 %. Thus, we see that both models can be ac-
cepted for prediction, but Holt's model provides higher accuracy of prediction.
Let's start with building an adaptive selective model. The essence of such an adap-
tive selective composition of models is as follows. At each step, several base models
are used to determine the predicted values, then the obtained values should be com-
pared with the actual ones. The model that showed better results is used to find new
predictive values. In the next step, the procedure is repeated.
In the previous stage, a forecast of a step forward, that is, for the 15th period, was
calculated using exponential smoothing and Holt models. Let’s compare the results
67
with the actual value, calculate M.A.P.E. and determine which model will be included
in the selective model forecast at this stage. In the first stage, we obtain the results
shown on Fig. 5.
Time Forecast
Actual value
period Exponential smoothing Holt model
5481,47 5637,04
15 5893 M.A.P.E.
6,983% 4,343%
Fig. 5. Actual values and predictive values for 15th period
Thus, in the 15th period, the best result was shown by the Holt model, this result will
be used for the selective model. From the same algorithm, we build a step-by-step
adaptive model of the average wage in the Kharkiv region. The results are presented
in Table.1.
Table 1. Step by step calculation and best model choice
Time Exponential smoothing Holt model
Actual value
period Forecast M.A.P.E. Forecast M.A.P.E.
15 5893 5481,47 6,98% 5637,04 4,34%
16 5848 5851,85 0,07% 6170,42 5,51%
17 5945 5848,38 1,63% 5980,13 0,59%
18 6468 5935,34 8,24% 6026,27 6,83%
19 6449 6414,73 0,53% 6779,87 5,13%
20 6224 6445,57 3,56% 6629,68 6,52%
21 6660 6246,16 6,21% 6156,58 7,56%
22 6593 6618,62 0,39% 6818,83 3,43%
23 6634 6595,56 0,58% 6682,48 0,73%
24 7447 6630,16 10,97% 6675,20 10,36%
Forecast
25 period 7365,3156 7892,407
We see that the chosen combined method of model construction justifies its im-
portance, because at certain stages of model development, the quality of the forecast
changes significantly and the models are interchangeable, thereby covering the under-
medication at each stage and improving the quality of the forecast. Thus, the selective
adaptive model has the following data, which is given in Table 2.
68
Table 2. Selective adaptive forecasting model results
Time period Actual value Selective adaptive model Final model choice
15 5893 5637,04 Holt
16 5848 5851,85 ES
17 5945 5980,13 Holt
18 6468 6026,27 Holt
19 6449 6414,73 ES
20 6224 6445,57 ES
21 6660 6246,16 ES
22 6593 6618,62 ES
23 6634 6595,56 ES
24 7447 6675,20 Holt
M.A.P.E. 4,569%
According to UkrStat Forecast
25* 7789 7892,40 Holt
(June 2018)
M.A.P.E. 2,65%
We see that the forecast value, which compares with the known actual value of the
average wage for the first month of 2017, has a small margin of error and excellent
forecast quality. A graphical comparison of the actual values with the calculated val-
ues is presented in Fig. 6.
6000
5000
4000
3000
У Yфактичний (грн)
– actual values
2000
1000 Адаптивна селективна
adaptive selective model
модель
0
0 5 10 15 20 25
Fig. 6. Actual and calculated values of Index
The developed adaptive selective model made it possible to build a better model
than the models provided separately. So, the shortcomings of one model can be
blocked by another, thereby increasing the result.
Comparison of the forecast quality of the developed models is presented in Fig. 7.
69
7%
6,036%
6% 5,691%
Адаптивна селективна
Adaptive selective
5% модель
model
4,569%
4%
Експоненційне
Exponential smoothing
згладжування
3%
2% Медель Хольта
Holt model
1%
0%
Fig. 7. Forecast quality comparison
We see that due to the developed selective model we managed to increase the effi-
ciency and quality of the forecast by 1.52 times. In this case, this is a great result,
since a change of 1% means a big change in the original data. With the help of an
adaptive selective model, a 2-step forecast has been constructed. According to the
same methodology, all other regions are forecasted for the other 14 indexes, which
was determined from the previously constructed study models [8]. The set of regional
socio-economic unevenness indexes is formed according to the following factorial
groups of indicators: social and demography, foreign economic activity (x4 – Number
of marriages, x14 – Average monthly nominal wages of full-time employees, x18 –
Number of households with children, x26 – Incidence of active tuberculosis, x29 –
Number of detected crimes, x40 – Reset contaminated return water in surface water
objects, x46 – Retail turnover, x55 – Mobile subscribers, x60 – Total imports of ser-
vices), economic resulting and financial potential (x43 – Gross regional product per
capita, x44 – Cost-effectiveness of operating activities of enterprises, x47 – Capital
investment per capita, x51 – Volume of sold industrial products (goods, services) per
person), agricultural potential (x50 – Labor productivity in agricultural enterprises).
The forecast will provide an opportunity to predict the state of socio-economic de-
velopment of the region, as well as to estimate the overall level of unevenness. Fore-
casted value of indicators of social and economic development of regions for 2018
and 2019 are shown at the table. 3, 4.
70
Table 3. Estimated values for the social potential group
Indexes
№ Region
x4 x14 x18 x26 x29 x40 x46
1 Vinnitska 11105.7 8247.5 218.7 498.3 13304.1 1 49780.6
2 Volinska 6963.7 7861 159.6 521.1 12396.8 1 30448.9
3 Dniprope-
trovska 24112.8 9290.2 456.7 1737.8 44563.2 235 133948.2
4 Donetska 5101.4 10813.2 237.3 952.5 28876.2 143.6 39845.5
5 Gitomirska 8721.1 7806.4 180.7 612.4 15812.9 3 38726.1
6 Zakarpatska 8281.4 8883 192.1 667.9 9628.1 3.9 37847.2
7 Zaporigska 12114.1 8904 246.5 822.7 49901.9 61.9 67143.2
8 Ivano-Fran-
kivska 8744.7 7716.9 213.7 664.7 10722.2 1 47521
9 Kyivska 15634.9 9393.9 244.1 1059.7 37277.6 5.1 82948.5
10 Kiro-
vogradska 6411.7 7622.9 136.6 658.2 18333.3 1.7 31278.6
11 Luganska 1183 8209 96.5 314.8 12654.7 19 6543.3
12 Lvivska
17451.6 8524.1 375.7 1032.9 40890.8 46.3 93593.4
13 Mykolaivska
8081.8 8964.7 172.6 557.8 15987.8 21.2 40978.5
14 Odeska 20392.9 9135.6 340.5 2529 36504 28.7 116794
15 Poltavska 10335.8 9027.6 185.9 682.2 23964.2 3.7 46027.7
16 Rivnenska 7323.6 8195.4 177.4 360.2 11975.4 6 30138.4
17 Sumska 6761.9 7981 150.4 561 15301.3 24 33314.2
18 Ternopilska 6146.3 7354.3 163.2 280 7041.7 2 25298.4
19 Kharkivska 20830.2 8415 371.7 975.9 63900.1 11 118224.2
20 Khersonska 7709 7814.4 142.4 721.8 17076 1 38633.2
21 Khmelnitska 8597.6 8277.6 185.2 497.7 13108.7 1 36235.4
22 Cherkaska 7930.3 7913.2 173.4 552.3 22040.8 7.2 39931.9
23 Chernivetska 6046.7 7861.7 154.8 264.3 10430.9 2 22661.2
24 Chernigivska 6451 7948.2 142.5 534.3 15668.8 6.1 29611.1
Table 4. Estimated values for the economic and agricultural potential groups
Indexes
№ Region
x55 x60 x43 x44 x47 x51 x50
1 Vinnitska 1225.9 12.7 66259.4 13.7 9072.3 53826.8 374167.5
2 Volinska 1150 18.7 45347.1 4.3 8267.9 32279.1 392304.2
71
3 Dniprope-
trovska 4033.1 181 96464.1 5.5 16114 153478 307816
4 Donetska 5868.4 198.2 34582.1 -2.4 3228.7 61535 293479.1
5 Gitomirska 908.2 12.3 52649 9.2 8056.4 37087.4 328044.4
6 Zakarpatska 1157.3 13.6 32073.3 7.8 5372.6 20134.2 157698.8
7 Zaporigska 2104.3 54.7 81324.5 12.8 11341.1 101827 230907
8 Ivano-
Frankivska 1265.6 16 47718.7 5.6 8010.6 41141.2 283321.3
9 Kyivska 1248.3 115.1 100817 4.3 23290.3 78337.8 258188.4
10 Kiro-
vogradska 1057.2 6.7 65861.8 7.3 9395.1 29906.6 220972.2
11 Luganska 2548.1 23.3 11231.3 -9.1 1799.7 7543.45 245346.4
12 Lvivska
2197.1 48.2 61430.9 6.3 11786.3 40027.6 489314.8
13 Mykolaivska
1343.3 53 68045.4 6.3 12374.7 54705.8 233176.7
14 Odeska 3078.9 197.2 66369.4 3 11358.9 32875.3 244867.3
15 Poltavska 1653.9 121.1 105284 8.5 13413.9 161166 229374.4
16 Rivnenska 1026.8 19.5 44702.5 2.1 6430.9 35922.8 367367.4
17 Sumska 1310.6 42.3 56250.3 16.3 8045.2 40842.4 341233.9
18 Ternopilska 604.6 9.2 38455 6.8 8374.6 18629.1 469373.8
19 Kharkivska 3989 36.3 76867.6 5.2 8470.3 76243.9 296067.2
20 Khersonska 1307.1 10.7 50067 9 8606 35424.2 282400.4
21 Khmelnitska 769 13.9 51433.6 14 10557.2 36291.4 400251.4
22 Cherkaska 1091.5 10.8 65479.9 11 8374.3 55330.3 288584.1
23 Chernivetska 956.5 1.4 29559.9 3.4 3569.8 159937.3 247513
24 Chernigivska 1098.9 20.3 56532.8 8.2 8988.1 61322.8 324271.9
Let's look at the dynamics of the predicted values of social potential indicators for
regions from the group with high potential of development (see Table 5)
Table 5. Predicted values increments of social potential indicators for regions from the group
with high potential of development
Region
Peri- Dne- Za-
№ Indicator Do- Khar-
od prope- porizhz Kyiv Lviv Odessa
netsk kiv
trovsk hya
Number 25 1,120 0,780 1,097 1,119 1,059 1,099 1,081
x4
of marriages 26 1,022 0,578 1,024 1,110 1,028 1,084 1,079
x14 Average wage 25 1,259 1,252 1,196 1,197 1,214 1,246 1,264
72
26 1,064 1,113 1,085 1,092 1,099 1,121 1,066
Number 25 0,990 0,882 0,990 0,997 0,995 0,996 0,994
x18 of households
26 0,990 0,901 0,988 0,994 0,998 0,998 0,995
with children
Number
of patients 25 0,965 0,947 0,924 0,960 0,881 0,993 0,883
x26
with active
tuberculosis 26 0,865 0,872 0,872 0,952 0,864 0,994 0,969
Number
25 0,997 1,005 1,034 1,082 1,029 1,021 1,069
x29 of crimes
detected 26 0,986 0,991 1,025 1,078 1,049 1,021 1,070
Water pollu- 25 0,999 0,935 0,985 1,040 0,970 0,942 0,909
x40
tion level 26 0,984 0,919 0,998 0,975 1,015 0,983 1,100
Retail 25 1,081 1,018 1,072 1,098 1,102 1,092 1,078
x46
turnover
26 1,075 1,036 1,066 1,090 1,095 1,089 1,071
Mobile 25 0,986 0,966 0,972 0,856 0,909 0,978 0,965
x55
subscribers 26 0,980 0,966 0,969 0,841 0,903 0,971 0,969
Import 25 0,924 0,887 1,009 1,014 1,135 0,972 0,905
x60
of services 26 0,766 1,119 1,048 0,741 0,729 1,107 0,903
Thus, Kyiv region is the most important, which is the leader in this classification of
regions. The Dnipropetrovsk region should be mentioned next. Donetsk region has the
lowest values in 2018-2019 (25 – 26 period). Since this region is not economically
stable, it is likely that it will move to the second class - with low level of socio-
economic development.
5 Discussion and Conclusion
According to the research results it was proved that the current stage of development
of the Ukrainian economy is characterized by structural imbalances of regional devel-
opment, manifested in the unbalanced growth rates of groups of donor and recipient
regions, unbalanced growth rates of economic and social spheres of different regions.
Significant regional disparities are a deterrent to ensuring high rates of economic
growth throughout the country. Thus, the analysis of the uneven socio-economic de-
velopment of the regions of Ukraine made it possible to conclude that the problem is
highly relevant.
The possibilities of adaptive smoothing techniques for the prediction of multidi-
mensional objects have been analyzed in the paper. Advantages and disadvantages of
existing methods of predictive analytics were shown. An attempt is made to build
selective models, the composition (basic set) of which includes several simpler adap-
tive models. The selective adaptive model is based on a combination of the exponen-
73
tial smoothing model and the Holt model. In combined models of the selective type,
at each step, automatic selection by the given criterion of the best model is organized.
Thus, adaptation takes place at two levels: level 1 (according to the structure of the
model or type of model) and level 2 (according to the parameters of the model). In the
combined hybrid model, the forecast is formed as a weighted sum of forecasts ob-
tained by alternative models. The weighting coefficients of smoothing are adaptive in
this case. An adaptive selective model for predicting indicators of uneven socio-
economic development of regions was developed based on Data Science methods.
The suitability analysis of models for forecasting the values of unevenness level of
socio-economic development of regions was conducted. Prospects for further research
include the possibility of identification of the most significant strategic levers of bal-
ancing regional development disproportions This provides the basis for identifying
priority vectors for crisis management in the region, achieving a proper economic
status, further sustainable development of both individual regions and the country as a
whole.
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