**Published at : ** 29 Dec 2023

**Volume :** **IJtech**
Vol 14, No 8 (2023)

**DOI :** https://doi.org/10.14716/ijtech.v14i8.6839

Eremina, I., Rodionov, D. 2023. The Special Aspects of Devising a Methodology for Predicting Economic Indicators in the Context of Situational Response to Digital Transformation.

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Irina Eremina | Peter the Great St.Petersburg Polytechnic University, St. Petersburg, Polytechnicheskaya, 29, 195251, Russia |

Dmitriy Rodionov | Peter the Great St.Petersburg Polytechnic University, St. Petersburg, Polytechnicheskaya, 29, 195251, Russia |

Abstract

The
methods currently used for detecting situational deformations in the time
series of economic indicators have a number of major flaws, which encourages
further research and development in this field aimed at improving the quality
and stability of the regression models in the context of digital
transformations. The purpose of this research is to devise a methodology for
predicting economic indicators in the context of situational response to digital transformation. We examine methods for
predicting economic indicators through time series analysis, following which
the vector of proactive development can be determined. In order to achieve our
objectives, we employed various methods, including mathematical statistics,
mathematical modeling, numerical methods, and regression analysis. Our analysis
of seasonality in the time series of economic indicators, given the cyclic
dominance and modified series, allows us to conclude the need for their
structural decomposition with proactive data rejection and modifications and
considering their possible displacement. We devised our own original
methodology for better processing of statistical data and improved stability of
linear regression models ineffective forecasts in the context of situational
response of digital transformations. The statistical tools we
suggest are likely to enhance the quality of the economic forecasts obtained
with the use of regression models (from 15%) due to the preliminary processing
of source data and determination of the cyclic dominance of the modified
series. The study shows that the methodology for predicting
time series in the context of situational response offers the fastest and most
accurate data analysis.

Cyclic dominance; Linear regression; Model prediction methodology; Situational response; Structural modifications

Introduction

Since economic research uses lots of data today, and
the results of their analysis are essential, it is really important to get
prompt situational responses to digital transformation.
If we ignore situational changes that occur in modern economic processes, it
can result in a significantly worse quality of the mathematical model and
consequently, the real economic situation can be distorted (Egorov *et al.*, 2021). The purpose of this
study is to develop a methodology for predicting economic indicators in the
context of situational response to digital transformation.
The subject of the research is the methods applied for predicting economic
indicators with time series and subsequent formation of a vector of proactive
development. The
scientific novelty of the study is the methodology we propose

Experimental Methods

**Literary Review**

Forecasting
is also very different in terms of its content (demography, society, economy,
environment, natural resources, etc.) (Nazarychev, Marinin, and Shamin, 2022). Various
sources of information can be utilized in forecasts, including accumulated
experience that involves understanding the fundamental laws of the phenomena
being investigated (Babkin
*et al.*, 2021), extrapolation of the existing trend (Egorov *et al.*, 2021), building
models of the projected phenomena and objects in the expected conditions (Tanina *et al.*, 2022). Depending
on their purpose, forecasts can be normative and exploratory. The former use
pre-set goals and define deadlines and ways to achieve them. Exploratory
forecasts, on the contrary, follow the trends in the past development of a
phenomenon in order to predict its future development (Pishchalkina, Pishchalkin, and
Suloeva, 2022). Economic
forecasting is helpful in solving several important tasks in the context of
situational response (Zhogova
*et al.*, 2020). First, there is a need for a scientifically sound
and, at the same time, objective picture of future processes based on current
indicators. Secondly, the directions of economic activities to choose from must
consider forecast estimates. Thirdly, we should identify the present factors
that will influence the phenomena we study. For this study, the analysis of
today’s forecasting methods and models with adaptation to situational changes
is very important. In this regard, forecasting that uses time series is
essential for economic performance prediction. Quantitatively, this dependence
can be measured using a linear coefficient of correlation between the levels of
the original series and those of the same series, which are shifted by several
steps in time (Hao,
2022). There are many ways and approaches to considering
the unavoidable error in the modeling of the time series of economic indicators
(Rusanov, Abbazov, and Baluev, 2022; Lemeshko and* *Lemeshko, 2005). Considering
situational change results in building a model, each level of which is a fuzzy
number of a triangular type, whose modal value coincides with the relevant
discrete value of the clear model, while the carrier of a fuzzy number contains
(there is a certain value of the probability function) the value of the
corresponding level of a real series (Zainy *et al.*, 2023). Authors
cope with the extreme fluctuation of past data due to COVID-19 and other world
events in several ways. 1. Acknowledging and addressing the limitations.
Authors are aware of the limitations posed by the drastic changes in data and
its impact on their research. They acknowledge the uncertainties and potential
biases introduced by the fluctuations and make efforts to address them. 2.
Offering alternative scenarios or projections. Authors may present alternative
scenarios or projections to account for the uncertainties caused by the events (Prasetya, Yopi, and Tampubolon, 2023). 3.
Conducting additional research. Authors may conduct additional research to
update their data and analysis to include the latest information and reflect
the impact of the events under consideration
(Grishunin *et
al.*, 2022). Thus, the fuzzy model takes into account the error
of situational change in economic processes.

**Methods and Materials**

We used the
STATISTICA 10.0 software package for calculations. This system can make fairly
accurate forecasts in different areas. STATISTICA uses various forecasting
methods (Boginsky,
2021). If this difference exceeds a certain threshold, it
means there are structural deformations in the data. Situational deformations
can be removed from a sample if it contains a sufficient amount of data for
analysis and the representativeness of the sample is not reduced. Otherwise,
various adjustment methods are used (Egorov *et al.*, 2021). The main ones are
manual substitution (used it there are not many structural measurements) (Sandler and* *Gladyrev, 2020); substitution for
the most probable value (Saroji
*et al.*, 2022); data interpolation (substitution of structural
transformations with the values obtained from similar samples) (Zubkova *et al.*, 2022); proactive
smoothing of the data (Zaytsev *et al.*, 2021; Agus *et al.*,
2021). In our study, we
employed the STATISTICA 10.0 software package along with several mathematical
tools to identify the seasonal component in a dynamic series. This involved
seasonal correction using Seasonal Decomposition 1, the X11 Seasonal
Decomposition module, and the Multiple Regression module. Additionally, we
utilized these tools to assess the stability of linear regression models, which
included rejecting certain data points and implementing modifications within
the context of situational response. This process encompassed building relevant
modifications and forecasts while considering confidence interval bias. The author’s
methodology for time series forecasting in the context of situational response
includes several main stages: Stage 1. Identify and analyze the seasonality of
economic indicators. Stage 2. Improving the stability of linear regression
models based on data rejection and its modifications in the context of
situational response. This method involves randomly selecting subsets of the
data multiple times, training the model on each subset, and evaluating its
performance. The average performance across all iterations provides an
indication of the model's generalization capability.

Results and Discussion

**Results**

The author’s
methodology for time series forecasting in the context of situational response
includes several main stages.

**Stage 1. Identify and analyze the
seasonality of economic indicators.** The methodology was
tested during the analysis of Russia's average per capita monetary income. The
evaluations are aimed at proactive forecasting in the context of situational
response: 1. The series data of the indicator are visualized: the population’s
average per capita monetary income for the timely determination of seasonality.
2. The trends of seasonality are determined using the method of Seasonal
Decomposition 1 in the context of situational economic development. 3. The
seasonality of the economic indicator is identified using the X11/Y2k method
(Census 2). As a starting point for further application of
Seasonal Decomposition 1 in order to carry out timely seasonal adjustments in
the context of situational response, we will analyze the time series of the
Russian population’s average per capita monetary income, data for the period
from the first quarter of 2013 to the second quarter of 2022. According to the
results obtained, there are undulating deterministic periods in the fourth
quarter, and a minimum value is observed in the first quarter. We move on to
the next task, which is aimed at strengthening the study in terms of identifying
the seasonality of the economic indicator based on the X11/Y2k method (Census
2).
In order to build an effective qualitative model, the source data have
to be preliminarily processed so that anomalous measurements can be identified
in them. It is shown that regression analysis is an important tool for
analyzing experimental data, whose private but effective instrument is linear
regression. Given the identified features of cyclic dominance and the formed
modified series, we find it reasonable to expand our scientific approach by
increasing the stability of the linear regression models based on data
rejection and modifications in the context of situational response.

**Stage 2. Improving the stability of linear
regression models based on data rejection and its modifications in the context
of situational response.**

The
following ones are most commonly applied as the criteria for estimating the adequacy
of a paired linear regression model: 1) the
coefficient of determination R2 reflects the proportion of variance of the
dependent variable explained by regression. In other words, it shows a part of
the values of regressor X, which fully explains the behavior of random variable
Y with the constructed regression equation. It can take values from 0 to 1. The
stronger the dependence between random variables X and Y, the closer the value
of the coefficient of determination is to 1, indicating a better fit of the
model to the data. Additionally, the F-test is employed to estimate the
significance of the regression equation. Based on the data obtained, for a
timely situational response, it is proposed to introduce a module of the
displacement magnitude of the forecast result, which appears as a result of the
original equation correction and changing the type of the new equation after
data rejection and its modifications in the context of situational response and
further maintaining of proactive development trend of the time series. The
author’s mathematical model, based on data rejection and its modifications in
the context of situational response, will have the following form equation (1):

where is the
linear regression equation before situational response; is the
linear regression equation after situational transformations (data rejection
and modifications)

Tables 1 – 2 present the results of the method used for increasing the stability of linear regression models due to data rejection and modifications in the context of situational response. The tables contain the values of the coefficients of determination R2 and accuracy T, calculated using a model obtained after rejecting some statistical data in the context of situational response. The quantity of the rejected observations corresponds to the probability of non-occurrence in a given area. Table 3 shows the displacement magnitudes of the estimated forecast value and the values of the confidence interval. The advantages of the first modification of the method where some data is rejected in the context of situational response are: 1) it can be used for multidimensional linear regression models; 2) there is no binding to a specific amount of data, i.e., the value of coefficient k does not change depending on the sample size, while the value of t in this method changes in case the amount of data changes too; 3) simplicity. The proposed method does not require additional calculations or tables.

**Table
1 **Values of displacement magnitude ? and confidence
interval *(calculated by the authors)*

As can be
seen from the table, when using the proposed method aimed at improving the quality
of regression models based on changes in the values of situational
deformations, the coefficient of determination R2 increases from 0.55 to 0.79.
This value is achieved by changing the values of five observations. Thus, it
can be concluded that good results can be obtained using the method where
situational deformations of time series are searched for and subsequently
corrected by applying data displacement and modifications, as well as using the
method based on data rejection. Table 2 shows the displacements of the
estimated forecast value and the confidence interval values. When applying this
second modification to the processing of statistical observations, it is
recommended to eliminate no more than 15-20% of the initial values. A larger
quantity of eliminated values may suggest that the data exhibit a certain
regularity and are not significantly affected by structural deformations.

**Table
2 **Values of the bias and confidence interval (CI) indicator
for linear regression models based on data rejection and its modifications in
the context of situational response *(calculated
by the authors)*

This example (which considers the relationship between the population’s per capita monetary income and the average nominal wage, the size of the population (at the beginning of the year), investments in fixed assets, and current prices) shows that the displacement value, given the deformation transformations, is equal to 31306.6. This observation is the next-to-last value of the variation series and has been chosen to visually display the magnitude of displacement in the context of situational response since, at this point, the magnitude of displacement will be significantly greater than at a point equal to the average value of the magnitude. We do not use the last observation of the variation series because it may appear anomalous and far removed from other values of the variation series. As can be seen from the table, positive results are obtained when using the proposed method of detecting and eliminating structural deformations. Once a reliability area is established with a confidence probability of 0.9 for the data within this range, structural measurements can be identified. Applying the method, we can reveal two anomalous observations in this case. Their exclusion from the sample allows us to increase the coefficient of determination from 0.55 to 0.69. Determination coefficient R2 reaches its maximum value with a confidence probability of 0.65 (7 rejected points) and amounts to 0.83. At the same time, if only 4 values are rejected, the value of the coefficient of determination can grow to 0.79, which also indicates the adequacy of the linear regression model in this case. It should be highlighted that these 4 observations are the observations that have been changed in the initial sample for us to run the experiment. If the first modification of the method is used, the maximum value of R2 reaches 0.876 when 7 observations are rejected. However, the abnormal value is not detected because it is quite close to the trend line. Therefore, despite the higher value of the coefficient of determination, in this case, it is preferable to use the method that increase the stability of regression models based on data rejection. The idea of the second method that should improve the accuracy of the regression model is that at the first stage, the same as in the previous method based on data rejection, the boundaries of the area of reliable data are found. Unlike in the first method, the data that do not fall into the area with a given probability are not excluded from the sample but, instead, are moved to the boundaries of this area, resulting in a change in their values. The second modification of the method applied for this experiment allows us to increase the value of R2 to 0.61 by rejecting the two extreme anomalous observations. In all three cases, the value of the bias does not exceed 9%, and the value of the confidence interval goes down compared to the initial one. The first modification demonstrates the minimum displacement value. This is due to the fact that, in this case, one of the structural transformations of independent variable X is not detected. The computational complexity is low, and the average running time of the algorithm is minimal, so the proposed methodology can be used for other indicators. It can be said that positive results are achieved when we apply the forecasting methodology based on using time series in the context of situational response, determining the seasonality of the cyclic dominance of modified series, and using data rejection and modifications with the possibility of their displacement.

**Discussion **

Modern
literature describes algorithms for applying various methods to adapt to
situational changes (Lemeshko
and* *Lemeshko,
2005). The
following ones are among the most common: Grubbs's test, the Titien-Moore-Beckman
method, the Acton and Prescott-Lund methods, and Cook’s method. We should agree
with other scientists that the main advantage of these methods is their
simplicity in terms of understanding and application (Kredina *et al.*, 2022). The great
strength of these methods is that they can be used to estimate several
situational deformations in the sample at once. However, if several values are
studied concerning situational response, a value that is not an outlier may
fall under suspicion, and other methods will have to be used to check a
specific value. Also, the Titien-Moore-Beckman criterion has the same
disadvantage as Grubbs’s test. The second degree is used when estimating the
criterion statistics, which reduces the accuracy of calculations (Prasetya, Yopi, and Tampubolon, 2023; Rodionov and Velichenkova, 2020). The
Titien-Moore-Beckman criterion assumes that the number of k outliers is known
in advance, but this is not always the case. The problem in identifying the
number of outliers is considered by the Rosner criterion (Tanina *et al.*, 2022). Due to the
fact that Cook’s method allows you to reject several source data at once, let
us compare this method with the modifications of the methodology developed by
the author of the present work. Table 3 shows the results of a comparative
analysis of the author’s methodology for predicting time series in the context
of situational response and Cook’s method.

**Table 3 **The results
of a comparative analysis of the author's methodology for predicting time
series in the context of situational response and Cook’s method *(calculated by the authors)*

A comparative analysis of the author’s methodology for predicting time series in the context of situational response and Cook’s method produced the following results: in terms of the R2 criterion, the method based on data rejection is preferable. Cook’s method trails to it by 10%; in terms of the magnitude of the displacement modulus of the forecast result, Cook’s method turns out to be better. When rejecting such sets of measurements, the R2 magnitude sharply decreases (Cook’s criterion is silent about this). This is due to the essence of Cook’s criterion, which is aimed at blind (in case a computer is used) tracking of the minimum magnitude of the total In the machine version, Cook’s criterion can be applied only together with the R2 criterion. Thus, our methodology offers better results for almost all criteria and is quite simple when applied in modern computer technologies, whereas Cook’s method is difficult to formalize due to its great computational complexity and the lack of a formal criterion for identifying the impact of specific observations. When searching for anomalous values using the Acton method, a suspicious value Y =46,359 was found at X = 29,946, as the largest deviation of the initial measurements from the predicted data.

After that, the value was calculated and compared to
the critical one. Since the calculated value turned out to be greater than the
critical one, the value is recognized as a situational deformation. This method
is intended for checking one suspicious value, but 2 more values were checked
as an experiment. One of them turned out to be an outlier: Y=45,644.07 at X
=32,285. Next, the Titien-Moore-Backman method was used to search for the
anomalous value. A suspicious value was identified. The value obtained by the
criterion was 2.71, but it turned out to be less than the critical value for
the significance level of 0.1, so, according to this method, the suspicious
value is not an outlier. The third was the Prescott–Lund method. We used it to
obtain a value of 2.69, which is less than the critical value of 2.72.
Therefore, this value is not recognized as an outlier. Figure
1** **presents the results
of the comparative analysis. As can be seen from
the figure, the methodology proposed by the author is suitable for identifying
a greater number of situational deformations in the time series compared to
other methods. This result is achieved in 445 elementary operations.

**Figure 1** The results
of a comparative analysis of the effectiveness of situational deformations
determined using the most common methods (developed by Acton,
Titien-Moore-Backman, Prescott-Lund, Cook) and the author’s methodology for
predicting time series in the context of situational response *(calculated by the authors).*

Two anomalous
observations are detected by the Acton method, and none are detected by the
Titien-Moore-Beckman or Prescott-Lund methods. Cook's method turned out to be
the closest to our method in effectiveness. However, three situational
deformations were identified using the former method. Besides that, the number
of elementary operations grows if the number of suspicious values that are
being checked is increasing. There is no specific criterion for which of the
suspicious values should be recognized as deformations. Thus, the existing
methodologies for predicting economic indicators in conditions of adaptation to
various structural deformations have a number of serious drawbacks.
Consequently, the methods used in the scientific literature have a number of
common disadvantages, which can be eliminated if the author’s methodology is
applied: the methods are poorly formalized and adapt only to similar
situational transformations at each step; most of them are used only for
one-dimensional samples, i.e. there is a situational response only for one-time
series; there are no specific recommendations on researcher’s further actions
after structural deformations have been found in the time series; common
methods of responding to certain situations rely on specific laws of a
probability distribution, and yet, they are not known at the initial level (Rodionov and Velichenkova, 2020; Lemeshko and*
*Lemeshko,
2005). The
methodology proposed by the author for improving the processing of initial
statistical data and increasing the stability of linear regression models for
more effective forecasts in the context of situational response offers a
comprehensive approach to modeling and a capacity to smooth out situational
deformations of time series as well as the level of seasonality.

Conclusion

The algorithm
ensures better quality of economic forecasts obtained using linear regression
models (from 15%), due to the preliminary processing of the source data and
identification of the cyclic dominance of the modified series. In this case,
the increase in the termination coefficient can be from 15% to 30% due to the
process of data rejection and structural modifications. The study shows that
the methodology for predicting time series in the context of situational
response offers the fastest and most accurate data analysis procedure suitable
for detecting any situational deformations. The author’s methodology, which
implies detection and further change of the measurement values, increases the
stability of linear regression models and makes forecasts more effective in the
context of situational response. It offers you a comprehensive approach to
modeling where situational deformations of time series can be smoothed out, and
the level of seasonality for samples of a small size is reduced because, unlike
a method where the data is simply excluded, with this approach, the initial
amount of data is preserved. The mathematical tools proposed in this paper for
improving the stability of regression models are to be used in further research
for nonlinear regression predictive equations with internal linearity based on
structural transformations and reduction to a linear form.

Acknowledgement

The research was financed as part of the project
"Development of a methodology for instrumental base formation for analysis
and modeling of the spatial socio-economic development of systems based on
internal reserves in the context of digitalization" (FSEG-2023-0008)**.**

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