Forecasting the prospects for the development of regional small business

. Small business is an integral part of the region's economy, and without its participation it is impossible to imagine the development of the region's economy. Small business, with its mobility and wide coverage, contributes to the sustainable and sustainable development of the region's economy. The relevance of the topic under study is due to the need to assess the impact of small business activities on regional socio-economic development. The purpose of the study is to analyze on the basis of ionometric modeling the state of future phenomena and processes in the activities of small businesses in Surkhandarya region. To achieve this goal, the methods of statistical and econometric analysis were used in the article, in which, based on indicators representing the development of small entrepreneurship, GRP, as well as the Arima model (an autoregressive econometric model integrated into the moving average of the gretl software package), the relationship between effective and factor indicators in quantitative and qualitative forecasting of proposals and recommendations is analyzed.


Introduction
The competitiveness of small business entities in the conditions of the modern economy will be associated with the forecasting of the activities of the enterprise.It is possible to clearly see in advance the goals of the activities of small business entities, quickly adapt to the changing conditions of the external environment, ensure the stability of entrepreneurial activity [1] through the correct distribution of material and human resources [2].
The fundamental essence of the decree of the president of the Republic of Uzbekistan "Тhe development strategy of the New Uzbekistan for 2022-2026."alsoprovides for the rapid development and high growth rates of the national economy, protection of the rights and legitimate interests of business entities, creation of conditions for the organization of entrepreneurial activity and the formation of permanent sources [3].
During the meeting, the parties discussed issues related to compliance with regulatory legal acts, as well as issues related to compliance with regulatory legal acts.
It should be noted that the determination of the perspective of the state of the employee and processes that may occur in the future provides for a scientifically based and qualitative data analysis, which is carried out on the basis of forecasting.In this case, the choice of forecasting method is considered important.The accuracy of the forecast is the criterion for evaluating the forecasting method.In order to increase the accuracy of the forecast, forecasting methods are being improved today.
The determination of the prospects for the development of the potential of small business entities is carried out by forecasting.In this case, the main goal is to find the most optimal ways of future development prospects using indicators and scientific methods that reflect the features of the development of small businesses.Forecasting the potential of small business entities of the territory is carried out for long, medium and short-term periods.Taking into account the current situation in the economy, a model of socio-economic development of the territory is formed on the basis of the development of a market strategy for the activities of small business entities.When forecasting the potential of regional business entities, the correct choice of the forecasting method plays an important role.

Literature review
Today, forecasting the socio-economic development [4] of small entrepreneurship is becoming relevant as a necessary tool in the development of state and territorial programs [5] of various levels of entrepreneurship.The correctness, accuracy of assessing the types and degree of risk associated with the implementation of management decisions in the development of entrepreneurial activity is considered to be among the first issues.By modeling future situations, it becomes possible to determine the possible danger that may arise.
For evaluating the socioeconomic growth of the operations of small business organizations, there are two main approaches: an approach based on economic and mathematical modeling and a system of integral indicators that are computed using an average geometric formula.
Such methods are used in a lot of scientific studies.In this study, a variety of economic variables were utilized to evaluate the main challenges and opportunities for the growth of small enterprises.
It is feasible to rate the contribution of business entities to the socioeconomic development of the territory using the approach created by A.E. Kremin [6].
For evaluating the efficacy of small entrepreneurship, the multi-factor regression analysis equation has been utilized in certain research [7].However, utilizing dynamic econometric models to analyze the relationship between the GDP and the small company production rate was not given special consideration in these studies.
O.N. Bulakina underlines that when evaluating the effectiveness of State programmes intended to develop and support small business, as well as contributing to increasing their growth potential, it is essential to take into account integrated indices which are representative of state and entrepreneurship development [8].
The Almon method, which also includes the multidirectional aproximability of lag structure, is very important in today's development of econometric models and forecasting parameters for Socioeconomic Development of Small Business Entities.In this way, the flexibility of a vector of coefficients for structural lag parameters and their number of forecast parameters is reduced.Figure shows how lag structures are distinguished using polynomials.It is called lag Almon under the name Almon [9].
The model is an instrument to eliminate adverse trends and situations, as described in the process of determining the advantages and disadvantages of alternatives strategies for developing a study entity, which has been considered one of the most useful tools with respect to analysis of factors.Here, the following circumstances explain why it is important to model and forecast development of entrepreneurship: -the need to correctly assess the changing market dynamics, the behavior of competitors in the domestic and foreign markets when making rational management decisions in conditions of constant fluctuations in economic dynamics; -the reason why forecasting is considered to be the first stage in the implementation of long-term plans and programs is that many processes that are considered the main factors of reproduction have a high degree of uncertainty.
The results of research on forecasting show that there is no single forecasting method, in practice they are interconnected and are composed of complementary methods: extrapolation, modeling, covering elements such as expert opinion [10].
As we know, econometric forecasting methods belong to the category of analytical methods that allow you to determine the parameters of various indicators, including socioeconomic forecasting, as well as analyze the quality of forecasts obtained on the basis of certain formal statistical criteria.Forecasting is the result of assessing the future values of indicators calculated on the basis of certain mathematical models, the probability of which is expected using the data obtained.The result obtained in the modeling process does not represent the final expression of the idea of the description of the process under study, but shows what values the indicator will receive if the factors included in the model are preserved.Also, the model taken as the basis for the forecast should be considered the most optimal at the request of various levels of criteria.This means that the obtained forecast values reflect the best result about the future state of the observed indicator.
In the process of forecasting the main parameters for the development of the potential of small businesses, the choice of the most optimal forecasting methods is of particular importance.The methods of induction, deduction are often widely used in the analysis of the potential of Small Business Objects.In forecasting economic processes, the induction method is used to obtain probable results in conditions where there is no sufficient information or long-term statistical data.
In conditions of reliable and inadequate information about the market situation, an expert assessment can give a good result when small business entities receive the necessary forecast data on the state of the future business sector in the event of a large uncertainty in their activities.Therefore, when forecasting the development of the entrepreneurial sphere, special attention should be paid to socio-economic processes that are under the strong influence of political and foreign economic factors.Individual expert methods aimed at assessing the development of small entrepreneurial activity are based on the development of analytical assessments by independent experts.

Materials and methods
The methodological basis of this research work is the development of an econometric model, which represents the relationship between the YHM and the small business production cost using econometric models, in which it is necessary to evaluate the relationship between the resulting and factor indicators using the scenario forecasting method using the ARIMA (integrated autoregression model for the sliding medium) model of the GRETL econometric software consists of.In it, the tasks of determining the significant relationship between the production costs of the NSC and small business, assessing the quantitative parameters of this dependence, developing methods for their scenario forecasting are set.
A distinctive feature of the scenario forecasting method is that it makes it possible to simultaneously study several possible development options related to entrepreneurial activity.Co-founder of the scenario forecasting methodology.Kahn believes that simple extrapolation methods may not have a good effect in forecasting certain processes [11].The use of the scenario method allows business entities to objectively assess changing situations in economic dynamics, identify possible threats that may arise, areas of stable activity, as well as adapt to changing situations in the economy.Forecasting is a complex process of planning the development of economic systems and implies the possibility of linking the factors of the current and past periods with future probabilities.
As you know, the large-scale application of modeling in economic analysis and forecasting is explained by the following circumstances: -first, there is the possibility of separating and formal writing the somewhat important and significant relationships of economic variables and objects that are abstracted at an extremely complex high level; -secondly, from relations with clearly expressed foundations, primary data and methods of deduction, conclusions can be obtained that correspond to the model of relations and adequate representations included in statistical parameters; -thirdly, the methods of mathematics and statistics provide for the acquisition of new knowledge about the appearance and form of the relationship between induction methods and variables that correspond to the object under study at a high level; -finally, fourth, the use of the language of mathematics makes it possible to clearly and compactly explain the rules of economic theory, express its essence and conclusions.
Scenario forecasting methods are common in Western countries (Germany, USA, etc.).The effectiveness of scenario forecasting is explained by several factors (Figure 1).

Fig. 1. Levels for assessing the effectiveness of the scenario forecasting method
Scenario forecasting allows business entities to coordinate and prepare in advance strategic plans that will be implemented in various crisis situations that may occur in the future.

Results
We decided to develop forecast values for the next five years of the prospects for the development of territorial small business activities using the method of scenario forecasting.One of the common methods for developing forecast values is the trend method, but it depends only on time and does not have the ability to fully express changes, in addition, determining the type of model corresponding to the indicator also acquires complexity.Furthermore, in practice it has also been widely accepted to define the Multifactor production function on the basis of influence factors as well as forecast indicators which are dependent on changes in factor content.Given that there is now a growing public awareness of using econometric package software, in our study we also dealt with the issue of determining Levels for assessing the effectiveness of the scenario forecasting method Allows small businesses to be prepared for certain situations that may arise in the future.This preparation will increase the rate of response of the business entity to changes in the conditions of instability, and ultimately the level of competitiveness of the entrepreneurial structure will increase Scenarios determine which factor the situation is developing according to and encourage you to be prepared for this process Scenarios make it possible to clarify strategic plans in advance using certain indicators in conditions of uncertainty forecast indicators from an ARIMA integrated autoregressive model for GRETL Dasuri's sliding medium suite.In the ARIMA model (p,d,q) there is an order in which prepresents the autoregression parameter, d is the integration part, q is the sliding mean parameter.In practical econometric studies, the following types of this order are widely used: 1) p=0, d=1, q=1 2) p=0, d=2, q=2 3) p=1, d=1, q=1 4) p=1, d=1, q=0 5) p=2, d=1, q=0 On each of the above procedures, analyzes are carried out in a computer program, choosing the most optimal for the forecast model.
However, when carrying out econometric analysis, it is required to focus on the most primitive type of data and the issues of using methods suitable for them.We decided to use the ARIMA models when developing forecast indicators, taking into account the fact that time series are used in the study.Within the framework of the study, the aim is to develop forecast values for the total products created by small business and entrepreneurships (SBI) in Surkhandarya region until 2026.For this, data from 2005-2020 were used.
We used the Gretl program to check the detected data for availability.According to the results, it was found that the first-rate difference in all cases is starsionar.For this reason, when developing forecast indicators, it was found that the results of the model in the form of ARIMA (1 1) are adequate in relation to others.
First of all, let's draw attention to the results of the model drawn up for the development of forecast values for the volume of production of total small business products (Table 1).The mathematical representation of this model can be written as follows.Here: SBI -the value of small business products produced in the Surkhandarya region at unchanged prices (at prices in 2005).From the data of table 3.2.2presented above, we can see that all the determined coefficients of the model are adequate.In particular, Akaike, Schwarz, Hannan-Quinn confirm that the criteria correspond to the requirements set for the practical implementation of the model.Based on the positive results presented, on the basis of this model, we developed forecast values of the volume of small business products of Surkhandarya region for 2026 (Table 3).For 95% confidence intervals, z(0.025) = 1.96 According to the results of the forecast, by 2026, the volume of production by small businesses in the Surkhandarya region will be 27681.5 billion soums at unchanged prices.That is, it means that the average annual growth rate was determined to be 5.3%, increasing 1.44 times compared to 2020.The study of the existing traditional forecasting methods can be seen that in most cases they are based on the processing of quantitative information and a separate consideration of parts of the system.Today, in the conditions of lack of necessary sources of information and instability of the external environment, their use in the entrepreneurial process may not have sufficient effect.In the 1970s, members of the International Organization "Club of Rome" D. Medouza, M. Mesarovich and E. Pestelya projected economic development trends using computer models.Von Reibnis believes that for the first time they revealed complex relationships and mutual ties in a clear sequence [11].
The main difference between a scenario forecast from the traditional method is that the actions of an entrepreneurial entity are based on several results, and not one [12].
In addition, to assess the forecasting potential of small businesses, it is necessary to take into account many factors affecting the actions of business entities, among which the most important ones can be noted: strengthening the role of business requirements in the digital transformation of the economy [13], the development of digital technologies [14] and robotics [15], the development of business ecosystems [16] and various technological devices [17], state control over the development of small business [18] and positive aspects of small business development [19], structuring of the economic space for small business [20], some opportunities for sustainable business development [21], including in the context of the coronavirus pandemic [22], solving problems of supply chain sustainability [23] and technological business development [24], improving the organizational and economic mechanism of innovative business development [25], supporting business development [26] and its analysis [27], cross-border succession of business [28] and the resolution of conflict relations between the subjects of the business process [29], the impact of external processes on the economic development of business [30] and the creation of social entrepreneurship [31], control over foreign companies [33] and business process management [34].
In order to improve the quality of forecasting the potential of small businesses, we propose to use a scenario forecasting method that allows you to assess the state of complex economic processes in advance.The application of a scenario forecast in situations characterized by the influence of various factors has shown that it is effective.Today, this method provides an in-depth analysis of the external and internal environment of the activities of small business entities, as well as their further sustainable development.

Conclusion
According to the calculations carried out, in the first scenario, the average growth rate at the time when the volume of production of small businesses is 12.8 percent.By 2025, the rate of economic growth is 1.03 times less than the highest forecast figure in previous years.This directly leads to the fact that it is necessary to pay attention to the level of growth of factors that directly affect the production costs of small businesses.
The second scenario is the small business production rate with an average growth rate of 4.7 percent over the years.By 2025, if the rate of economic growth is 1.01 times less than the highest forecast figure in previous years.Based on forecast indicators, there is a relatively low rate of growth in the first scenario.
In the third scenario, the forecast indicator for the small business production volume provides the most reliable forecast values in connection with the fact that it is calculated at a high level of accuracy on the basis of the Gretl software package.In this regard, forecasting the cost of small business production in Surkhandarya region on the basis of an econometric software package plays an important role in determining strategic directions with a high degree of accuracy.

Fig. 2 .
Fig. 2. The results of the forecast based on the ARIMA (1 1 1) model developed on the Real values of the volume of production of small business products in Surkhandarya region In order to express to what extent the results of this forecast are reliable, we cited the appearance in the form of a graph in Figure 2. The model is evaluated on the basis of which the true value with a value of close to one of the indicators of the reliability of forecasts based on serves.

Table 1 .
Dynamics of the volume of production of small-scale enterprises of Surkhandarya region.

Table 2 .
The results of the model ARIMA (1 1 1), developed according to the Real values of the volume of production of small business products in Surkhandarya region.ARIMA, observations 2006-2020 were used (T = 15).Dependent variable: (1-L) SBI Standard errors are calculated based on the Hessian

Table 3 .
The results of the forecast based on the ARIMA (1 1 1) model developed on the Real values of the volume of production of small business products in Surkhandarya region.

Table 4 .
Multi-scenario forecast of the small business production plant of Surkhandarya region by