Modern problems of science and education. Hello student Application of socio-economic forecasting in the preparation of decisions

Currently, not a single sphere of social life can do without forecasts as a means of knowing the future. Especially important are forecasts of the socio-economic development of society, substantiation of the main directions of economic policy, and foreseeing the consequences of decisions made. Socio-economic forecasting is one of the decisive scientific factors in the formation of the strategy and tactics of social development.

The relevance of this topic both in a developed market economy and in a transitional economy is determined by the fact that the level of forecasting the processes of social development determines the effectiveness of planning and management of the economy and other areas.

The purpose of this course work is to consider the methodology and techniques for developing socio-economic forecasts to determine the essence, areas of application and the most effective forecasting methods. To do this, it is necessary to solve the following tasks: to determine the essence of the methods of socio-economic forecasting and the area of ​​their application in the course of studying the theoretical and methodological foundations of the forecasting methodology; to characterize the methods of socio-economic forecasting in economically developed countries and to identify the features of their application in modern Ukraine.

In the process of writing this term paper, textbooks edited by V.O. Mosin, K.L. Triseeva, V. Tsygichko, V.V. Deniskin, as well as scientific articles on the problem under study in the periodicals "USA: Economics Politics Ideology", "World Economy and International Relations", "Problems of Forecasting", "Russian Economic Journal", "Problems of Forecasting", "Russian Economic Journal", "Economy of Ukraine", "Bulletin of Moscow State University".

Socio-economic foresight of the main directions of social development presupposes the use of special computational and logical methods that allow determining the parameters of the functioning of individual elements of the productive forces in their interconnection and interdependence. Systematized scientifically grounded forecasting of the development of socio-economic processes on the basis of specialized ones has been carried out since the first half of the 50s, although some forecasting methods were known earlier. These include: logical analysis and analogy, extrapolation of trends, polling the opinion of specialists and scientists.

In the development of the methodology for forecasting socio-economic processes, the scientific developments of domestic and foreign scientists A.G. Aganbegyan, I.V. Bestuzhev-Lada, L. Klein, V. Goldberg. The works of these scientists consider the meaning, essence and functions of forecasting, its role and place in the planning system, explore the issues of methodology and organization of economic forecasting, show the features of scientific forecasting. The development of works covering forecasting issues is carried out in the following main areas: deepening the theoretical and applied development of several groups of techniques that meet the requirements of different objects and different types of forecasting work; development and implementation in practice of special methods and procedures for the use of various methodological techniques in the course of a specific forecast research; search for ways and methods of algorithmic forecasting techniques and their implementation using a computer.

Forecasting methods should be understood as a set of techniques and methods of thinking that allow, based on the analysis of retrospective data, exogenous (external) and endogenous (internal) connections of the forecast object, as well as their measurements within the framework of the phenomenon or process under consideration, to derive judgments of a certain certainty regarding it (the object) future development.

According to estimates of domestic and foreign scientists, there are currently over 20 forecasting methods, but the number of basic ones is much less (15-20). Many of these methods relate rather to separate techniques and procedures that take into account the nuances of the predicted object. Others are a set of individual techniques that differ from the basic ones or from each other in the number of private techniques and the sequence of their application.

In existing sources, various classification principles of forecasting methods are presented. One of the most important classification features of forecasting methods is the degree of formalization, which quite fully covers forecasting methods. The second classification criterion can be called the general principle of the forecasting methods, the third is the method of obtaining forecast information. In fig. 1.1 shows the classification scheme of forecasting methods.

As shown by the diagram shown in Fig. 1.1, according to the degree of formalization (according to the first classification criterion), methods of economic forecasting can be divided into intuitive and formalized. Intuitive forecasting methods are used in cases where it is impossible to take into account the influence of many factors due to the significant complexity of the forecasting object. In this case, expert estimates are used. At the same time, individual and collective expert assessments are distinguished.

The composition of individual expert assessments includes: the “interview” method, in which direct contact between the expert and the specialist is carried out according to the “question-answer” scheme; analytical method, in which a logical analysis of any predicted situation is carried out, analytical reports are drawn up; a method of scripting, which is based on the definition of the logic of a process or phenomenon in time under various conditions.

The methods of collective expert assessment include the method of "commissions", "collective idea generation" ("brainstorming"), the "Delphi" method, the matrix method. This group of methods is based on the fact that with collective thinking, firstly, the accuracy of the result is higher, and secondly, when processing individual independent assessments made by experts, at least productive ideas can arise.

The group of formalized methods includes two subgroups: extrapolation and modeling. The first subgroup includes methods: least squares, exponential smoothing, moving averages. The second is structural, network and matrix modeling.

The considered classes of intuitive and formalized methods are similar in their composition to expert and factographic methods. Factographic methods are based on actually available information about the predicted object and its past development, expert methods are based on information obtained from the estimates of expert experts.

The class of expert forecasting methods includes the method of heuristic forecasting (heuristics is a science that studies productively creative thinking). This is an analytical method, the essence of which is the construction and subsequent truncation of the “search tree” of expert judgment using some heuristic. With this method, specialized processing of predictive expert assessments is carried out, obtained by a systematic survey of highly qualified specialists. It is used to develop forecasts of scientific and technical problems and objects, the analysis of the development of which either completely or partially does not lend itself to formalization.

In the studied literature, a significant number of classification schemes for forecasting methods are presented. The main error of such schemes is a violation of the principles of classification, which include: sufficient coverage of forecasting methods, the unity of the classification feature at each level of division (with multilevel classification), the non-intersection of classification sections, the openness of the classification scheme (i.e., the possibility of supplementing with new methods) ...

In most classification schemes, forecasting methods are divided into three main classes: methods of extrapolation, expert judgment and modeling. With such a division, the methods of extrapolation are opposed as an independent class of methods of modeling.

On the one hand, the construction of models aims to reveal the pattern of development of the object or process under study in a certain retrospective area. And if the model is built correctly and adequately reflects the connections and properties of a real object, it can serve as a basis for extrapolation, ie, for transferring some conclusions about the behavior of the model to the object. This is predicting the behavior of an object by extrapolating the trends identified in the model.

On the other hand, extrapolation methods are nothing more than the use of theoretical and empirical models to find variables outside the retrospective section of observations based on the data of the relationships between them in the retrospective section. Thus, the use of extrapolation in forecasting always presupposes the use of any models. Therefore, any modeling is the basis for extrapolation.

Constructive classification allows you to visually depict a set of forecasting methods in the form of a hierarchical tree and to characterize each level with its own classification feature. (fig. 1.2)

At the first level, all methods on the basis of "informational basis of the method" are divided into three classes: factual, combined and expert.

Analysis and forecasting of socio-economic development is the starting point of work on the management of regional development. On the basis of a well-grounded forecast, the goals of the socio-economic development of the region are determined, program measures and priorities in the development of the regional economic complex are specified. Forecasting the socio-economic development of a region is a prediction of the future state of the economy and social sphere, an integral part of state regulation of the economy, designed to determine the directions of development of the regional complex and its structural components.

The results of forecast calculations are used by state bodies to substantiate the goals and objectives of socio-economic development, develop and substantiate the socio-economic policy of the government, ways to rationalize the use of limited production resources. The forecast of the socio-economic development of the region includes a set of private forecasts reflecting the future of certain aspects of society, and a comprehensive economic forecast, reflecting in a generalized form the development of the economy and social sphere of the region.

Private forecasts estimate:

• demographic situation in the region;
• the state of the natural environment, including such areas as proven reserves of natural resources, land, water and forest resources;
• the future state of scientific and technological achievements and the possibility of their introduction into production;
• main factors of production (capital, labor, investment);
• the size and dynamics of the population's demand for goods and services;
• effective demand of the population for certain goods and
• services;
• the rate of development of individual sectors of the national economy, territories and other socially significant spheres of activity.

The comprehensive economic forecast reflects the future development of the region's economy as an integral entity. The development of a comprehensive forecast is based on scientific foundations that adequately explain the functioning and development of the regional economic complex. In terms of the time horizon, complex forecasts of the economic development of regions can be divided into three types: long, medium and short term.

The long-term forecast is developed every five years for a ten-year period. It serves as the basis for the development of the concept of socio-economic development of the country in the long term. In order to ensure the continuity of the economic policy being pursued, the data of the long-term forecast are used in the development of medium-term forecasts, concepts and programs of the country's socio-economic development.

A mid-term forecast of the country's socio-economic development is developed for a period of three to five years with annual data adjustments. It serves as the basis for the development of a concept for economic development in the medium term. For the purpose of general familiarization, the data of long- and medium-term forecast calculations, as well as the concept of socio-economic development, are published in the open press.

A short-term forecast of socio-economic development is developed annually and serves as the basis for drafting the state budget. The above documents are an integral part of the package submitted by the Government of Russia to the Federal Assembly.

This package includes:

• data on the socio-economic development of the country for the past period of the current year;
• forecast of socio-economic development for the coming year;
• draft consolidated financial balance sheet in Russia;
• a list of the main socio-economic problems (tasks) of development, which will be addressed by the policy of the Government of the Russian Federation;
• a list of federal targeted programs, planned for financing in the coming year from the federal budget;
• the list and volume of supplies of products for state needs according to the enlarged nomenclature;
• designing the development of the public sector of the economy.

Along with this, the Government of Russia presents draft laws that it considers necessary to adopt for the successful implementation of the outlined tasks. The following are used as working tools for a comprehensive forecast: extrapolation of past trends in the development of the economy and social sphere for the future, econometric calculations based on the data of the national accounting system, a system of macrostructural models, including a modified model of the input-output balance, a model of capital dynamics and investment in the real sector of the economy ... This model has not yet been completed and is used only for experimental forecast calculations. There are two fundamentally different approaches to forecasting economic objects: genetic and teleological.

Genetic approach is based on the analysis of the prehistory of the development of the object, fixes its fundamental factors that determine the features of development. On this basis, conclusions are drawn regarding the state of the predicted object in the future. This approach is more characteristic of "outside observers" of the ongoing processes. Targets of socio-economic development in this approach do not play a special role. The most prominent representative of this approach in our country was N.D. Kondratyev with his theory of "long waves".

Strategic planning of regional development.

A strategic development plan for a region is a management document that contains an interrelated description of various aspects of regional development activities.

The preparation of such a document provides for:

• setting goals for the development of the region;
• determination of ways to achieve the set goals;
• analysis of potential opportunities, the implementation of which will make it possible to achieve success;
• development of methods for organizing traffic for selected
• directions;
• substantiation of rational ways of using resources.

The strategic plan for the socio-economic development of the region is an indicative document that allows the administration of the region and the regional community to act together. This is not only a document of the administration, but to a greater extent of all subjects of the regional development process, including economic agents and participants in the political process. This is not a directive from above, directed from the regional administration to entrepreneurs and residents of the region, but a guideline developed with the participation of all agents of economic activity. Such a plan provides for balanced and coordinated actions of all actors to solve existing problems. It is a tool for building partnerships, a mechanism for identifying and implementing effective strategic actions in all spheres of life in the region.

The main characteristics of the strategic plan for the socio-economic development of the region include:

• highlighting the strengths and weaknesses of the regional economy, striving to strengthen, develop, form the competitive advantages of the region with a focus primarily on creating better living conditions for people;
• concise ideas and principles that guide producers of goods and services, investors, the administration and the public, helping them to implement decisions based on a vision for future development;
• partnership interaction of all regional forces.

A component of the strategic plan for the development of the region should be the administration's action plan attached to it for the implementation of the planned activities.

The stages of developing a strategic plan for the socio-economic development of the region include:

1) an assessment of the achieved level and features of the socio-economic development of the region, which also presupposes an analysis of the regional resource base of this development;

2) elaboration of a concept for the development of the regional economy, elaboration of scenarios for the modernization of the regional economy in order to adapt the latter to the new system of interregional ties and interdependencies;

3) selection and substantiation of directions for the future development of the region.

Definition of "poles" of regional development is the most important task in developing a strategy for the development of the region. The main direction of reforming the economy of most regions at the present stage is a gradual movement towards the formation of a new social order of the post-industrial type based on the use of new technological methods of production in a multi-structured socially oriented economic system with modern characteristics of the quality of life of the population and with an active role of state bodies in regulating the economy.

An important principle for the development of social sectors will be to reduce the pressure of these sectors on the regional budget with a simultaneous increase in funding for these sectors in the budget.

The main components of the strategy of socio-economic development should be:

Pursuing a targeted structural, scientific, technical and investment policy;

Solving social problems while reforming the economy;

Stimulating business activity in the real sector of the economy.

The well-to-do and the poor.

REGIONAL AND MUNICIPAL ECONOMY

COMPARATIVE ANALYSIS OF METHODS FOR FORECASTING SOCIO-ECONOMIC DEVELOPMENT OF THE REGION [on the example of the Belgorod region)

The article discusses economic and mathematical methods, econometric models and their application in practice. Based on the comparative analysis of econometric methods, an algorithm for developing forecasts for the development of the Belgorod region is proposed, recommendations for improving the methodological support of socio-economic forecasting are substantiated. The article reveals the features of modern forecasting methods, substantiates the necessity and expediency of their application.

Regression mathematical models are an effective tool for the analysis and forecasting of phenomena and processes affecting the economic development of the region. The advantage of regression models lies not only in the ability to determine a quantitative measure of dependence, but also in the study of the influence of various factors.

Key words: forecasting, forecast, economic development of the region, regression models, economic and mathematical methods, econometric models, economic modeling.

Analysis and forecasting of socio-economic development is the starting point of work in solving problems of managing sustainable development of the region. The relevance of this task is due to the study of the development of forecasts for the development of the Belgorod region, the construction of an econometric model, the use of which will create the basis for forecasting the gross regional product. On the basis of a well-grounded forecast, the goals of the socio-economic development of the region are determined, program measures and priorities in the development of the regional economic complex are specified.

Forecasting the socio-economic development of the region - foreseeing the future state of the economy and social sphere, an integral part of state regulation of the economy, designed to determine the directions of development of the regional complex and its structural components. The results of forecast calculations are used by state bodies to substantiate the goals and objectives of development, formulate and substantiate the social and economic policy of the government, ways to rationalize the use of limited production resources.

E.S. PRIVOROVA

Belgorod State National Research University

Pridvorova @ bsu.edu.ru

The forecast of the socio-economic development of the region includes a set of private forecasts reflecting the future of certain aspects of society, and a comprehensive economic forecast, reflecting in a generalized form the development of the economy and social sphere of the region. The forecasting process itself contributes to the organization of constructive interaction between science, business, public organizations and regional government bodies, the formation of agreed views on the problems and prospects for the development of the region. Forecasting is also of great importance in the theoretical aspect, as it is a kind of catalyst for numerous studies, improving their methodology.

In theory and practice of planning activities, a significant set of various methods for developing forecasts has been accumulated. The famous scientist Erich Jantsch has more than a hundred of them; in practice, only 15-20 methods are used as the main ones (Fig. 1).

In essence, the methods of modeling the socio-economic development of the region can be summarized in four main groups: expert judgment; modeling; normative method; extrapolation. The development of computer science and computer technology makes it possible to expand the range of forecasting and planning methods used. Economic and mathematical models based on combinations of methods are returning to the forefront.

System of forecasting and planning methods

Method "interview):"

Analytical and year

The method of collective idea generation "Brainstorming"

Delphi method

Commission method

Method and spelling ologache-

SKOGS NELSHE.

Scripting method

Foresight method

Average detection method

Method "363"

Heuristic МЄТ0Д

List method

Median method

Analysis method and risk assessment

Total detections method

Matrix model

Imitation

Optimal planning models

Network model

Zkeyemshnzak

ITSC ​​models

Pole-environment interaction model

Diffusion Models NOE BOTH

Sustainable development model

The tree model sang to her

Model of innovative sustainable development

Expert Modeling Noriative Extrapolacil

rating | - | -

economic

Balance

Normative

Programming method

St atypical

?. ISTOD ______

Budget

Cash flow forecast

1T N TP-GTG yagity forecast

Economics and mathematics epic model

Orrvyanionno-regression ptgrd i model

Integer program ї, і і ration

Input-output balance model

Historical methods. analogies and prediction by pattern

Function selection method

How many _______ averages ________

Exponential smoothing method

Adaptive anti-aliasing method

Construction 1) ЄNDE

Leading method

Envelope method

Dynamic series method

Method of NSh picks and business activity

Method of group accounting of arguments

Factorial analysis method

Least square method

Linear software worlds

Dei graphic ______ model _______

Rice. 1. Classification of forecasting and planning methods

Series History. Political science. Economy. Computer science. 2013. No. 1 (144). Edition 25/1

The compilation of predictive values ​​of criterion indicators and indicators entails the uncertainty of estimates. There are many ways to reduce the risks of uncertainty in estimates when making decisions, to verify forecast data. First of all, it is recommended to use the following complementary steps: justify the size of the investment; present possible results indicating the main assumptions of their achievement or likelihood (risk assessment); take into account the perceptions and preferences of regional and municipal socio-economic development based on the principles of sustainability; develop appropriate decision-making rules and strategies for investing in modernization and innovative transformations.

Forecasting methods are continually being enriched and improved. The choice of the forecasting method depends on the period for which it is necessary to make a forecast, the possibility of obtaining the corresponding initial data, the requirements for the forecast accuracy, the amount of information. A wide variety of forecasting methods are presented in the economic literature. So, the researchers say that the whole variety of forecasting methods is based on two approaches - heuristic and mathematical.

Heuristic methods are based on the use of phenomena or processes that do not lend themselves to formalization.

Mathematical forecasting methods are characterized by the selection and substantiation of a mathematical model of the process under study, as well as ways to determine its unknown parameters. In this case, the forecasting problem is reduced to solving the equations describing the given model for a given moment in time.

Among the mathematical forecasting methods, extrapolation methods stand out in a special group, which are simple, clear and easy to implement.

Currently, the most common and widely used in economics are methods of expert assessments. "Expert assessment is a formalized qualitative or quantitative assessment by experts of the characteristics of objects of application of the method of expert assessments and possible subsequent comparison of the objects under study according to the corresponding characteristics." Practically in all constituent entities of the Russian Federation, in the course of the formation of forecasts of the socio-economic development of the region for the medium term, these approaches are used to predict the main parameters.

Modeling methods include a forecast based on the study of the internal logic of logical models of the development of the phenomenon under study, on the analysis of the historical continuity of the development of science and technology and scenarios of the future (logical analysis of the hierarchy of goals, description of real options for their achievement and resource assessment).

Normative methods are planning methods based on the application of norms and standards to substantiate planning, program and forecast documents.

When making forecasts using extrapolation, one usually proceeds from statistically emerging trends in changes in certain quantitative characteristics of an object. Estimated functional systemic and structural characteristics are extrapolated. Extrapolation methods are one of the most common and most developed among the entire set of forecasting methods.

Using these methods, quantitative parameters of large systems, quantitative characteristics of economic, scientific, and production potential, data on the effectiveness of scientific and technological progress, characteristics of the ratio of individual subsystems, blocks, elements in the system of indicators of complex systems, etc. are extrapolated.

Extrapolation methods are the most common in forecasting. They are distinguished by simplicity, clarity and are easily implemented on a computer. A detailed description of the extrapolation forecasting method is given in the works of scientists.

The basis of extrapolation forecasting methods is the study of time series.

Analytical methods for the extrapolation of trends are based on the application of the least squares method to the dynamic series and the presentation of the pattern of development of the phenomenon in time in the form of a trend equation.

Currently, adaptive methods are considered one of the promising areas of forecasting. Adaptive methods are used in conditions of strong fluctuations in the equations of the time series and allow, when studying the tendency, to take into account the influence of the previous equations on the subsequent values ​​of the time series. These methods are considered in the most detail by the scientist.

In regional studies, the prospects for the development of a particular territory are necessarily studied. The development trajectory or the future state of the region as a whole and of individual economic objects, in particular, is determined using the following methods: extrapolation, expert assessments, analogies, regression and correlation analyzes.

The most important advantage of adaptive methods is the construction of self-correcting models capable of taking into account the result of the forecast made at the previous step. Let the model be in a certain state, for which the current values ​​of its coefficients are determined. Based on this model, a forecast is made. When the actual value arrives, the predicted value error is estimated. The forecasting error enters the model through feedback and participates in it in accordance with the accepted procedure for transition from one state to another. As a result, compensating changes are generated, consisting in adjusting the parameters in order to better match the behavior of the model with the dynamics of the series. Then the forecast estimate for the next point in time is calculated, and the whole process is repeated again.

Thus, the adaptation is carried out iteratively with obtaining each new actual point of the series. The model constantly "absorbs" new information, adapts to it and therefore reflects the development trend that exists at the moment. In fig. 2 shows a general scheme for constructing adaptive forecasting models.

Rice. 2. Scheme of constructing an adaptive forecasting model: y (1 :) - the actual levels of the time series;) ’g (/) (1) - the forecast made

at the moment I on G units of time (steps) forward; e (+1 - forecast error, obtained as the difference between the actual and forecast value of the point indicator (1 + 1)

2013. No. 1 (144). Edition 25/1

The speed of the model's reaction to changes in the dynamics of the process is characterized by the so-called adaptation parameter. The adaptation parameter should be chosen in such a way as to provide an adequate display of the trend while simultaneously filtering out random deviations. The value of the adaptation parameter can be determined based on empirical data, derived analytically, or obtained based on a sample method.

As an optimality criterion when choosing an adaptation parameter, the criteria for the minimum of the mean square of the prediction errors are usually taken.

Based on the considered features, let us define a group of forecasting methods, united by the general name adaptive.

Forecasting methods are called adaptive that allow building self-correcting (self-adjusting) economic and mathematical models that are able to quickly respond to changing conditions by taking into account the result of the forecast made in the previous step and taking into account the different information value of the levels of the series. Due to the noted properties, adaptive methods are especially successfully used for operational, short-term forecasting. The specified definition reflects the main characteristic features inherent in the considered approach. At the same time, the division into adaptive and non-adaptive models is often conditional.

At the origins of adaptive methods lies the exponential smoothing model. Suppose the time series model is:

y (= ax + e (, (1)

where ax = cop81 :;

E (- random non-autocorrelated deviations with zero mean and variance.

For exponential smoothing of the series, a recursive formula is used:

^ = ay (+, (2)

where is the value of the exponential average at time 1 :; a - smoothing parameter a = sop81 :, 0<а<1;

If we consistently use relation (1), then the exponential average can be expressed in terms of the previous values ​​of the levels of the time series:

^ = ay, + = ay, + p (ay (_x +) =

Ay, + aru, _x + /? 2 ^ _2 = ... = ay, + aru, _x + ap2y, _2 + ... + aDy „+ ... + / Γ £ 0 '

Thus,

^ = i]? + /? "W o, (3)

where n is the length of the row.

As η -> °° P ”-> 0, therefore

Thus, the value of $ turns out to be the weighted sum of all members of the series.

Moreover, the weights of the individual levels of the series decrease as they recede into the past, corresponding to the exponential function (depending on the "age" of the observations). That is why the value of I is called the exponential average.

To eliminate the excess weight attributed to E0, R. Wade proposed to modify the procedure.

Let E "0 = aE0, then EH = ay! + (1 - a) E" 0 = ay! + (1 - a) aE0.

Since the weight coefficients in the sum now do not give one, an additional factor is introduced, which is equal to the reciprocal of the sum of the coefficients:

'V, = s; --- \ - г [oxyi + (l - a) aS0].

Then at the first iteration with a = 0.1 the weight of the current level y is determined by the expression

change ------- = 0.526, and the weight of S0 is already equal to the smaller value ------ = 0.474.

With short-term forecasting, it is necessary to reflect the changes in the series and at the same time clean it up by filtering out random fluctuations. For this, the value of a should be assigned one of the intermediate values ​​in the range from o to 1. If, as a result of experimental calculations, the best value of a, close to 1, is obtained, then it is advisable to check the correctness of the choice of a model of this type.

Sometimes the search for this parameter value is carried out by iterating over the values ​​on the grid. In this case, the value of a is chosen as the optimal one at which the smallest error variance is obtained. In most econometric packages, for example, "Mesosaurus", SPSS, STATISTIKA and others, when building these models, the menu provides a branch "optimization" that implements the search for values ​​according to this scheme.

In the course of the study, a forecast was made for further changes in the industrial production index. This indicator characterizes the change in the scale of production in the compared periods and is one of the main indicators of industrial production in the Belgorod region.

To carry out the forecast, we use the extrapolation method based on the construction of trend models.

Data for building a trend model of industrial production in the Belgorod region for 1992-2011. are presented in table. 1 .

Table 1

Initial data for building a trend model of industrial production in the Belgorod region for 1992-2011.

Year Industrial production index of the Russian Federation Industrial production index of the Belgorod region

1997 101,0 106,0

1999 108.9 I5.3

2000 108,7 109,1

2001 102,9 110,1

2002 103,1 116,0

2003 108.9 10b, 2

2004 u8, o u6, z

2006 u6, z 112.8

2008 100,6 111,6

2010 108,2 110,0

2011 R4.7 R6.9

Based on the presented initial data (Table 1), four trend models were built, shown in Fig. 3-6.

Belgorod region - = - RF ------ Polynomial (Belgorod region)

Rice. 3. Polynomial trend of the industrial production index

Belgorod region

If, to predict a time series with a pronounced linear trend, use formula 5, which is based on an exponential smoothing model, then the model will usually give biased forecasts, i.e. systematic error. For such time series, it is advisable to use linear growth models that also use the exponential smoothing procedure. The predictive model is determined by the equality

Y AI = a ^, (5)

where ^ uDO is the forecast made at the moment? by g units of time (steps) forward;

al, 1 - estimate ah ,.

In these models, the forecast can be obtained using the following expression:

W0 = "and +" C6)

where al, s / -, - current estimates of the coefficients; t is the forecast period.

Belgorod Region - ■ - RF Logarithmic (Belgorod Region)

Rice. 4. Logarithmic trend of the industrial production index

Belgorod region

# & £ & & £ & & # / # $ & $ & / # $ / /

F- Belgorod region - ■ - RF - ■ Degree (Belgorod region)

Rice. 5. Power trend of the industrial production index of the Belgorod region

- ♦ - Belgorod region - ■ - RF Exponential (Belgorod region)

Rice. 6. Exponential trend of the industrial production index

Belgorod region

Table 2, we represent the equation of the polynomial, logarithmic, power-law, exponential models of the industrial production index of the Belgorod region.

table 2

Trend models of the industrial production index of the Belgorod region

Model type Building a trend model

Polynomial model V = -0.1448 X2 + 4.0849 * + 82.994

Logarithmic model y = 8.6212 1n (x) +86.856

Power-law model y = 87.24 x0'0862

Exponential model V = 93.819

Accuracy was assessed for adequate models. The accuracy of the model is characterized by the value of the difference between the value of the actual level and the value according to the constructed trend model.

To assess the quality of a one-factor model in econometrics, the coefficient of determination and the average approximation error are used.

The average approximation error is defined as the average deviation of the obtained values ​​from the actual ones according to the formula (7)

The admissible approximation error should not exceed 10%. The results of checking the accuracy of the model are shown in table. 3.

Table 3

Average relative errors of approximation of adequate models,%

Model type Error value Exact error value Accuracy level

Logarithmic 0.22 0.228 -

Power 0.22 0.220 Exact

Polynomial 0.22 0.220 Exact

Exponential 0.22 0.229 -

So, the most accurate is the power-law and polynomial trend model. Consider the forecast of the industrial production index of the Belgorod region for 2012-2013. in table. 4.

Table 4

Forecast of the industrial production index of the Belgorod region

for the period 2012-2013

Forecast Industrial Production Index

Logarithmic trend model Power trend model Polynomial trend model Exponential trend model

2012 113.10 P3.42 104.92 116.96

2013 113,50 113,88 102,77 118,19

The index of industrial production of the Belgorod region under these conditions according to the power-law trend model in 2012 is forecasted at the level of 116.96%, and in 2013 - at the level of 118.19%., According to the polynomial trend model, the index of industrial production in 2012 will be 104.92 %, and in 2013 - 102.77%.

Regression analysis methods are of great applied importance in forecasting the gross regional product in the Belgorod region. It was revealed that the advantages of the regression method should be considered its versatility, a wide range of functional dependencies, the possibility of including the time factor in the statistical model as an independent variable.

The best results are obtained with the multiple regression model:

Γ = a + bn + b2x2 + b3x3 + .... + b „xn, (8)

where Y is the dependent variable (gross regional product in the Belgorod region), x, - are independent variables (factors), b, - are regression coefficients.

The regression correlation coefficients are presented in table. 5.

The main criteria for the selection of factors are accuracy, reliability, efficiency of obtaining information, as well as the ability to predict them. Based on these requirements, the following factors were selected to build the model:

Population, thousand people (х1);

Extraction of minerals billion rubles (x2);

Consumer Price Index (x3);

Producer price index for industrial goods (хД

Table 5

Regression Coefficients and Correlation Coefficients

Independent variables Regression coefficients Correlation coefficients

Xi Population, thousand people 1.24 0.95

x2 Extraction of minerals, billion rubles 12.57 0.94

The initial data were used for the period 1995-2011. After determining the regression coefficients, the regression equation takes the following form:

Y = -18684.2- + 1.24 ^ + 12.57X2-1.83X3-1.2bx ^. (nine)

The correlation coefficient takes values ​​in the range from -1 to +1. If the coefficient is more than 0.7, the connection is strong or close. The strongest relationship is with the population factor. The determination coefficient for the model is R2 = 0.95.

The calculated correlation coefficient indicates a very close dependence of the change in gross output on the change in its factors. The coefficient of determination characterizing the quality of fitting a straight line regression for the forecast is 0.95. This suggests that the regression equation is explained by 95% of the variance of the effective trait, while other factors account for only 5% of the variance, i.e. residual variance.

Thus, we can conclude that in the course of the study, a forecast of further changes in the industrial production index was carried out. To implement the forecast, an extrapolation method was used based on the construction of trend models. Accuracy was assessed for adequate (valid) models. It was revealed that the most accurate is the power-law and polynomial trend model.

Bibliography

1. Berezhnaya, E.V. Mathematical methods for modeling economic systems / E.V. Berezhnaya, V.I. Berezhnaya. - M .: Finance and statistics, 2003.-368 p.

2. Dubrova, T.A. Statistical forecasting methods / T.A. Dubrova. - M .: UNITI-DANA, 2003.-206 p.

3. Egorov, V.V. Forecasting the national economy / V.V. Egorov. - M: INFRA-M, 2001.-184 p.

4. Nastenko, A. D. Forecasting sectoral and regional development / A.D. Wall-ko. - M: HeliosARV, 2002.-144 p.

5. Regions of Russia. Socio-economic indicators. 2002 - 2011: stat. Sat. M .: Rosstat, 2002 - 2011.

PREDICTION SOCIO-ECONOMIC DEVELOPMENT OF THE REGION)