In the process of financial forecasting, specific methods are used to calculate financial indicators, such as math modeling, econometric forecasting, expert assessments, trending and scenarios, stochastic methods.

Math modeling allows you to take into account many interrelated factors that affect the indicators of the financial forecast, choose from several options for the draft forecast the most appropriate for the accepted concept of production, socio-economic development and the goals of financial policy.

econometric forecasting based on the principles of economic theory and statistics: the calculation of forecast indicators is carried out on the basis of statistical estimated coefficients with one or more economic variables acting as forecast factors; allows you to consider the simultaneous change in several variables that affect the performance of the financial forecast. Econometric models describe, with a certain degree of probability, the dynamics of indicators depending on changes in factors that affect financial processes. When constructing econometric models, the mathematical apparatus of regression analysis is used, which gives quantitative estimates of the average relationships and proportions that have developed in the economy during the base period. To obtain the most reliable results, economic and mathematical methods are supplemented by expert assessments.

Method expert assessments involves the generalization and mathematical processing of assessments of specialist experts on a particular issue. The effectiveness of this method depends on the professionalism and competence of the experts. Such forecasting can be quite accurate, however, expert assessments are subjective, depend on the "feelings" of the expert and are not always amenable to rational explanation.

trend method, which assumes the dependence of some groups of income and expenses only on the time factor, proceeds from constant rates of change (trend of constant growth rates) or constant absolute changes (linear time trend). The disadvantage of this method is ignoring economic, demographic and other factors.

Scenario Development does not always come from scientific and objectivity, they always feel the influence of political preferences, preferences of individual officials, investors, owners, but this allows us to assess the consequences of the implementation of certain political promises.

Stochastic Methods assume the probabilistic nature of both the forecast and the relationship between the data used and the forecast financial indicators. The probability of calculating an accurate financial forecast is determined by the amount of empirical data used in forecasting.

Thus, the methods of financial forecasting differ in terms of costs and volumes of the resulting information provided: the more complex the forecasting method, the greater the costs associated with it and the volume of information obtained with its help.

Forecast Accuracy

The main criteria for evaluating the effectiveness of the model used in forecasting are the accuracy of the forecast and the completeness of the representation of the future. financial condition predicted object. The issue of forecast accuracy is somewhat more complex and requires closer attention. Forecast accuracy or error is the difference between the predicted and actual values. In each specific model, this value depends on a number of factors.

Extremely important role play the historical data used in the development of the forecasting model. Ideally, it is desirable to have a large number of data over a significant period of time. In addition, the data used should be "typical" in terms of the situation. Stochastic methods of forecasting, using the apparatus of mathematical statistics, impose very specific requirements on historical data, in case of non-fulfillment of which the accuracy of forecasting cannot be guaranteed. The data must be reliable, comparable, sufficiently representative for the manifestation of patterns, homogeneous and stable.

The accuracy of the forecast clearly depends on the correct choice of the forecasting method in a particular case. However, this does not mean that only one model is applicable in every case. It is quite possible that in some cases several different models will produce relatively reliable estimates. The main element in any forecasting model is the trend or line of the main trend of the series. Most models assume that the trend is linear, but this assumption is not always reasonable and may adversely affect the accuracy of the forecast. The accuracy of the forecast is also affected by the method used to separate seasonal fluctuations from the trend - addition or multiplication. When using regression methods, it is extremely important to correctly identify the cause-and-effect relationships between various factors and put these relationships into the model.

Before a model can be used to make realistic predictions, it must be tested for objectivity in order to ensure that the predictions are accurate. This can be achieved in two different ways:

The results obtained by the model are compared with the actual values after a certain period of time, when they appear. The disadvantage of this approach is that testing the "impartiality" of the model can take a long time, since the model can only be truly tested over a long time period.

The model is built from a truncated set of available historical data. The rest of the data can be used for comparison with the predicted figures obtained using this model. This kind of verification is more realistic, since it actually models the predicted situation. The disadvantage of this method is that the most recent, and therefore the most significant indicators are excluded from the process of generating the original model.

In light of the above regarding model validation, it becomes clear that in order to reduce the expected errors, it is necessary to make changes to an already existing model. Such changes are made throughout the period of application of the model in real life. Continuous changes are possible in terms of trend, seasonal and cyclical fluctuations, as well as any causal relationship used. These changes are then verified using the methods already described. Thus, the model design process includes several stages: data collection, development of the initial model, verification, refinement - and again all over again based on the continuous collection of additional data in order to ensure the reliability of the model.

Types of forecasts

There are three main types of forecast: technological, economic and forecast of sales (demand).

1. Technology Forecasts cover the level of development of scientific and technical progress or technological development in areas that directly affect the production in which the forecast is made. For example, a company producing computers is interested in the prospects for expanding the amount of memory on floppy disks, because. they are additional products for the use of computers, and an enterprise using harmful, toxic substances in its production is interested in developing technologies for waste treatment and disposal.

The development of scientific and technological progress leads to the emergence of new goods and services, and those, in turn, seriously compete with existing enterprises. A well-made forecast will save financial resources, predict the development of new technologies, even if scientific and technological changes have not affected the production of products.

2. Economic forecast allows you to predict the future state of the economy, interest rates and other factors affecting the development of any enterprise. Such decisions depend on the results of the economic forecast as: expansion or reduction of production capacities; conclusion of new contracts; dismissal or hiring of workers, etc.

3. Understanding the real level of demand on the company's products for a specific period in the future gives a forecast of sales. Such a forecast is the basis for planning and conducting economic calculations. Demand is influenced by many factors, which can be taken into account by making a forecast of sales volume (demand). As a basis for the future forecast, indicators such as the level of demand in the previous period, demographic changes, changes in the market shares of industry organizations, the dynamics of the political situation, the intensity of advertising, competitors, etc. are used.

In world practice, more than two hundred forecasting methods are used, while in domestic science - no more than twenty. The introduction indicated that the methods of financial forecasting, which are widely used in developed foreign countries, will be considered.

Thus, depending on the type of model used, all forecasting methods can be divided into three large groups (see Figure 1):

Methods of expert assessments, which provide for a multi-stage survey of experts according to special schemes and the processing of the results obtained using economic statistics tools. These are the simplest and most popular methods, the history of which goes back more than one millennium. The application of these methods in practice, usually, is to use the experience and knowledge of trade, financial, production managers of an enterprise or government agency. As a rule, this ensures that the decision is made in the simplest and fastest way. The disadvantage is the reduction or complete absence of personal responsibility for the forecast made. Expert assessments are used not only to predict the values of indicators, but also in analytical work, for example, to develop weight coefficients, threshold values for controlled indicators, etc.

Stochastic Methods, suggesting the probabilistic nature of both the forecast and the relationship between the studied indicators. The probability of obtaining an accurate forecast increases with the increase in the number of empirical data. These methods occupy a leading place in terms of formalized forecasting and vary significantly in the complexity of the algorithms used. The simplest example is the study of sales trends by analyzing the growth rates of sales indicators. Forecasting results obtained by statistical methods are subject to random fluctuations in data, which can sometimes lead to serious miscalculations.

Stochastic Methods can be divided into three typical groups, which will be named below. The choice for forecasting the method of one or another group depends on many factors, including the available initial data.

First situation- the presence of a time series - occurs most often in practice: a financial manager or analyst has at his disposal data on the dynamics of the indicator, on the basis of which it is required to build an acceptable forecast. In other words, we are talking about highlighting a trend. This can be done in various ways, the main of which are simple dynamic analysis and analysis using autoregressive dependencies.

Second situation- the presence of a spatial aggregate - takes place if for some reason there are no statistical data on the indicator or there is reason to believe that its value is determined by the influence of some factors. In this case, multivariate regression analysis can be used, which is an extension of a simple dynamic analysis to a multivariate case.

Rice. 1. Classification of methods for predicting the financial condition of an enterprise

Third situation- the presence of a spatio-temporal set - takes place when: a) the series of dynamics are insufficient in length to build statistically significant forecasts; b) the analyst intends to take into account in the forecast the influence of factors that differ in economic nature and their dynamics. The initial data are matrices of indicators, each of which represents the values of the same indicators for different periods or for different consecutive dates.

Deterministic Methods, suggesting the presence of functional or rigidly determined relationships, when each value of the factor attribute corresponds to a well-defined non-random value of the resultant attribute. As an example, we can cite the dependencies implemented within the framework of the well-known model factor analysis DuPont firm. Using this model and substituting predictive values into it various factors, for example, sales proceeds, asset turnover, degree of financial dependence, and others, you can calculate the predicted value of one of the main performance indicators - the return on equity ratio.

Others are very good example the income statement form is used, which is a tabular implementation of a rigidly determined factor model that links the effective sign (profit) with factors (sales income, cost level, tax rate level, etc.). And at the level of state financial forecasting, the factor model is the relationship between the volume of state revenues and the tax base or interest rates.

Here it is impossible not to mention another group of methods for financial forecasting at the micro level, based on the construction of dynamic simulation models of the enterprise. Such models include data on planned purchases of materials and components, production and sales volumes, cost structure, investment activity of the enterprise, tax environment, etc. The processing of this information within the framework of a single financial model makes it possible to assess the forecast financial condition of the company with a very high degree of accuracy. In reality, such models can only be built using personal computers, which make it possible to quickly perform a huge amount of necessary calculations.

Overview of basic forecasting methods

Modeling methods and economic and mathematical methods

Modeling involves the construction of a model based on a preliminary study of an object or process, highlighting its essential characteristics or features. Forecasting economic and social processes using models includes the development of a model, its experimental analysis, comparison of the results of predictive calculations based on the model with the actual data of the state of the object or process, correction and refinement of the model.

The methods of economic and mathematical modeling include the following methods:

matrix models (statistical and dynamic),
models of optimal planning,
economic and statistical,
· a lot of factor models,
econometric models,
simulation models,
models decision making,
Network planning models
the method of intersectoral balance,
· optimization methods,
Correlation-regression models.

Method economic analysis

Economic analysis is an integral part and one of the main elements of the logic of forecasting and planning. It should be carried out both at the macro-, and at the meso- and microlevels.

The essence of the method of economic analysis lies in the fact that the economic process or phenomenon is divided into its component parts and the interconnection and influence of these parts on each other and on the course of development of the entire process are revealed. Analysis allows us to reveal the essence of the process, to determine the patterns of its change in the forecast (planned) period, to comprehensively assess the possibilities and ways to achieve the goals.

In the process of economic analysis, such techniques as comparison, grouping, index method are used, balance calculations are carried out, normative and economic-mathematical methods are used.

balance method

The balance method involves the development of balances, which are a system of indicators in which one part, characterizing the resources by source of income, is equal to the other part, showing the distribution (use) in all directions of their expenditure.

In the transition period to market relations, the role of predictive balances developed at the macro level increases: the balance of payments, the balance of income and expenditure of the state, the balance of cash income and expenditure of the population, the consolidated balance of labor resources, balances of supply and demand. The results of balance calculations serve as the basis for the formation of structural, social, financial-budgetary and monetary policy, as well as the policy of employment and foreign economic activity. Balances are also used to identify imbalances in the current period, open unused reserves and justify new proportions.

Normative method

The normative method is one of the main methods of forecasting and planning. In modern conditions, it began to be given special importance in connection with the use of a number of norms and standards as regulators of the economy. The essence of the normative method lies in the feasibility study of forecasts, plans, programs using norms and standards. With their help, the most important proportions, the development of material production and the non-production sphere are substantiated, and the economy is regulated.

Forecast Accuracy

The main criteria for evaluating the effectiveness of the model used in forecasting are the accuracy of the forecast and the completeness of the presentation of the future financial condition of the forecasted object. The issue of forecast accuracy is somewhat more complex and requires closer attention. Forecast accuracy or error is the difference between the predicted and actual values. In each specific model, this value depends on a number of factors.

An extremely important role is played by historical data used in the development of a forecasting model. Ideally, it is desirable to have a large amount of data over a significant period of time. In addition, the data used should be "typical" in terms of the situation. Stochastic methods of forecasting, using the apparatus of mathematical statistics, impose very specific requirements on historical data, in case of non-fulfillment of which the accuracy of forecasting cannot be guaranteed. The data must be reliable, comparable, sufficiently representative for the manifestation of patterns, homogeneous and stable.

Before a model can be used to make realistic predictions, it must be tested for objectivity in order to ensure that the predictions are accurate. This can be achieved in two different ways:

These changes are then verified using the methods already described. Thus, the model design process includes several stages: data collection, development of the initial model, verification, refinement - and again all over again based on the continuous collection of additional data in order to ensure the reliability of the model.

At the micro level- at the level of an enterprise, organization (firm), the objects of forecasting and planning are: demand, production of products (performance of services), the need for material and labor resources, production and sales costs, prices, income of the enterprise, its technical development. The results of forecasts are the basis for making managerial decisions.

Subjects of forecasting and planning- planning and financial bodies of the enterprise, marketing and technical departments.

Forecast plans are developed both for the enterprise as a whole and for its structural divisions: workshops, sections, services.

The company distinguishes the following types plans:

Strategic plans- general business development plans. In the financial aspect, these plans determine the most important financial indicators and proportions of reproduction, characterize investment strategies and opportunities for reinvestment and accumulation. Strategic plans determine the volume and structure of financial resources required for the operation of the enterprise.

Current plans are developed on the basis of strategic ones by detailing them. If the strategic plan gives an approximate list of financial resources, their volume and directions of use, then within the framework of the current planning, each type of investment is mutually agreed with the sources of their financing, the effectiveness of each possible source of financing is studied, and financial assessment the main activities of the enterprise and ways to generate income.

Operational plans- these are short-term tactical plans directly related to the achievement of the company's goals (production plan, plan for the purchase of raw materials and materials, etc.).

Forecasting the future development of an enterprise is the most significant and difficult stage in preparing a business plan, since based on the results of predictive calculations of future market changes, costs, prices, profits, the scope of the project and the required resources are determined.

When forecasting financial performance, it is advisable to use a system of methods: expert assessments, extrapolation methods, factor models, optimization methods, normative method.

Thus, depending on the type of model used, all forecasting methods can be divided into three large groups (see Figure 1):

Rice. one . Classification of methods for predicting the financial condition of an enterprise

Deterministic Methods, suggesting the presence of functional or rigidly determined relationships, when each value of the factor attribute corresponds to a well-defined non-random value of the resultant attribute. As an example, we can cite the dependencies implemented in the framework of the well-known DuPont factor analysis model. Using this model and substituting into it the forecast values of various factors, such as sales proceeds, asset turnover, the degree of financial dependence, and others, it is possible to calculate the forecast value of one of the main performance indicators - the return on equity ratio.

Another very illustrative example is the income statement form, which is a tabular implementation of a rigidly determined factor model that connects the effective attribute (profit) with factors (sales income, cost level, tax rate level, etc.). And at the level of state financial forecasting, the factor model is the relationship between the volume of state revenues and the tax base or interest rates.

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MINISTRY OF EDUCATION OF UKRAINE

ZAPORIZHIA STATE TECHNICAL UNIVERSITY

CHAIR OF INTERNATIONAL ECONOMIC RELATIONS

EXPLANATORY NOTE

TO THE COURSE WORK ON THE DISCIPLINE "International Information"

Analysis of forecasting methods

Supervisor:

abstract

Explanatory note: 28 pages, 7 drawings, 1 formula, 9 sources

Object of study: forecasting methods.

Objective: study forecasting methods and analyze them

Research methods: deduction, system-structural

Research results: in the process of work, an analysis of forecasting methods was carried out, some theoretical aspects certain methods, the scope of forecasting methods, and specific example extrapolation method and trends were presented.

Keywords Keywords: forecasting, extrapolation, expert methods, heuristics, information, technology, information processing

Introduction………………………………………………………………………………….6

1. Tasks and principles of forecasting…………………………………………7

2. Methods of scientific and technical forecasting …………………………11

2.1 Classification of forecasting methods………..………………….11

2.2 Extrapolation forecasting methods……………………….13

2.3 Statistical methods…………………………………………………………16

2.4 Expert methods………………………………………………………… 17

2.4.1 Scope of expert methods………………………………………17

2.4.2 Heuristic forecasting method (IEP)…………………..19

3. Classification of economic forecasts……………………………..23

Conclusion………………………………………………………………………………….28

List of links………………………………………………………………………29

List of abbreviations

Feasibility study - table of expert assessments

PEO - personal expert assessment

MEP - heuristic forecasting method

COMPUTER - electronic computer

ECVM - electronic central computer

MHD - magnetic dynamic installations

NTI - scientific and technical information

INTRODUCTION

The forecasting process is quite relevant at the present time. The scope of its application is wide. Forecasting is widely used in economics, namely in management. In management, the concepts of "planning" and "forecasting" are closely intertwined. They are not identical and do not replace each other. Plans and forecasts differ from each other by time limits, the degree of detail of the indicators contained in them, the degree of accuracy and probability of their achievement, targeting and, finally, the legal basis. Forecasts, as a rule, are indicative, and plans have the power of directives. Not substitution and opposition of plan and forecast, but their correct combination - this is the way of systematic regulation of the economy in a market economy and the transition to it.

In industry, forecasting methods also play a paramount role. Using extrapolation and trend, it is possible to draw preliminary conclusions about various processes, phenomena, reactions, operations.

Forecasting also occupies a certain niche in military disciplines. Using forecasting methods, it is possible to determine (estimate) the radioactive situation of the area, etc.

There are many forecasting methods. Differentiating them total number, it is necessary to choose the best one for use in each specific situation.

Analysis of forecasting methods, study of these methods, their use in different areas activity is an action of rationalization character. The degree of reliability of forecasts can then be compared with really real indicators, and, having drawn conclusions, proceed to the next forecast with existing data, i.e. existing trend. Based on the data obtained, it is possible to move to a higher level in the time aspect, etc.

1. Tasks and principles of forecasting

Forecast - a specific prediction, a judgment about the state of a phenomenon in the future based on a special scientific study. The classification of forecasts is carried out, as a rule, according to two criteria - temporal and functional. On the basis of time, forecasts are distinguished: short-term, medium-term, long-term and extra-long-term. The functional classification of forecasts involves their division into research, program and resource.

Forecasting is the process of developing forecasts. Depending on the type of forecast, there are normative, search, operational.

Predictive model - a model of the object of forecasting, the study of which allows obtaining information about the possible states of objects in the future and (or) the ways and timing of their implementation

To obtain information about the future, it is necessary to study the laws of the development of the national economy, to determine the reasons, the driving forces of its development - this is the main task of planning and forecasting. The main driving forces for the development of production are social needs, technical capabilities and economic feasibility. In accordance with this, three main tasks of planning and forecasting can be pointed out: setting goals for the development of the economy; finding the best ways and means to achieve them; determination of the resources necessary to achieve the set goals.

Choice of goals is the result of an analysis of the socio-political tasks that need to be solved in society and which reflect the objective nature of the operation of economic laws.

The choice of goals is preceded by the development of alternative goals, the construction of a hierarchical system or a “tree of goals”, the ranking of goals, and the choice of leading links. The initial prerequisites for the choice of goals are, on the one hand, the real possibility of solving this alternative, and on the other hand, its optimality according to the efficiency criterion.

Ways and means to achieve goals are determined on the basis of an analysis of the development of the national economy and scientific and technological progress. At the same time, in in the process of forecasting, the area is limited alternatives ways and means to achieve the set goals, i.e., the area of optimal solutions is determined. In the process of developing a plan (making a decision), a single solution is determined that is optimal according to the accepted vector of criteria.

Depending on what task is solved in the first place, two types of forecasting are distinguished: research (or search) and normative. The formation of a forecast of objectively existing development trends based on an analysis of historical trends is called research or search forecasting. This type of forecasting is based on the use of the principle of development inertia, in which the forecast is oriented in time according to the scheme “from the present to the future”. A research forecast is a picture of the state of the forecast object at a certain moment in the future, obtained as a result of considering the development process as a movement by inertia from the present time to the forecast horizon. Forecasting trends in the development of the object of the forecast, which should ensure the achievement of certain socio-political, economic and defense goals at a given moment in the future, is called normative. In this case, the orientation of the forecast in time occurs according to the scheme "from the future to the present."

The discrepancy between normative and research estimates of the object of the forecast at each moment of time in the future is a consequence of the contradiction "needs - opportunities". A complex forecast is built on the basis of a composition of research and normative forecasts.

The choice of goals and means to achieve them must necessarily be combined with determining the need for resources. When determining this need, one should consider planned and forecast matrices of resources (financial, labor, material and energy), as well as matrices of production capacities and time resources. Both the required resources and the probable restrictions on their value in the range of the lead time of the plan or forecast are subject to assessment. Forecast resource matrices are the most important initial data in compiling the balances of the national economy in long-term planning.

The driving forces of development do not act in isolation, they are interconnected and interdependent and can be represented as a connected triangle graph:

Figure 1.1 Relationship of driving forces of development

The vertices of this "causal triangle" identify the driving forces of the development of production, its edges are mutual connections between them. Therefore, the tasks of planning and forecasting cannot be considered in isolation. In the process of forecasting and developing a plan, an analysis of the interaction of goals, methods and technical means their achievements, the resources necessary for their implementation, and the optimal ways of developing the national economy are determined according to the adopted efficiency criteria.

Despite the commonality of tasks, their formulation in forecasting and planning is different. When planning, the following scheme operates: "the goal is directive, the ways and means of achieving it are deterministic, resources are limited." When forecasting, the scheme is different: "goals are theoretically achievable, ways and means of achieving them are possible, resources are probable." Forecasting tasks differ in breadth of coverage. Forecasting problems should be assessed as global. These include: analysis of the situation, determination of information reliability levels, determination of the degree of probability, development of current, medium and long-term forecasts. Forecasting principles: a combination of socio-political and economic goals; democratic centralism; consistency; continuity and feedback; proportionality and optimality; reality and objectivity; highlighting the leading link, etc.

Forecasting must be systemic character. The need for a systematic approach to forecasting stems from the peculiarities of the development of science and technology, the national economy during the scientific and technological revolution. The scientific and technological revolution has led to a fundamental change in the properties, characteristics and structure of modern technology and the national economy. The growth in the number of elements, objects of various nature, the complexity of the relationships between them and the behavior of the object in the external environment led to the creation of large technical and production (organizational-economic) systems.

Modern machines have a high structural and functional complexity, they are technical complexes that include a huge number of parts, assemblies, assemblies and finished products united by a finite functional integrity. Structural and functional complexity causes high material consumption, labor intensity, energy intensity and cost of technical complexes. The development of technology has led to the creation of complex hierarchical structural constructions - large technical systems. This property of technical complexes required a systematic approach to its creation, system design. In the developed technical complexes, the designs of individual incoming elements must be subordinated to the common goal for which the system is created, i.e., a single strategy for the behavior of the technical system must be provided.

The creation of large technical systems, in turn, caused the emergence of large organizational and economic (production) systems, covering many enterprises united by the release of a certain technical complex. There is a hierarchy in the management structure manufacturing enterprises. The steadily increasing pace of development of science and technology, the creation of modern organizational and economic systems have led to an avalanche-like growth of information and an increase in the degree of irregularity of its receipt. All this required the improvement of planning methods, the creation of a planning system.

The most important requirements of a systematic approach are the complexity of forecasts and plans and the continuous nature of the planning process.

An integrated approach provides for the preparation of forecasts and plans in conjunction both in space (in the sectoral and territorial context) and in time. The relationship in space means the establishment of rational relations between sectors of the national economy, economic regions, the establishment of optimal ratios between the rates of development of science, technology and industrial production, the balance of needs and resources at all levels of the hierarchy.

The relationship of forecasts and plans in time is ensured by the implementation of the principle of planning continuity. Correction of plans and forecasts should be discrete in nature with advance deadlines(functioning mode). A relatively frequent change in plans, causing a change in production programs, can lead to disorganization of the work of industries and enterprises due to the complexity of the structure of production relations in the national economy, the high labor intensity and material intensity of the processes of preparing industrial production.

The sensitivity of the forecast and plans to changes depends on the level of the hierarchy, the timing of the lead and the frequency of adjustments. The lower the level, the higher the sensitivity, the shorter the correction periods should be.

The most important point in the introduction and use of continuous planning systems is to determine the quality of such systems and, on the basis of this, find optimal mode functioning.

Planning continuity is ensured by implementing the feedback principle. Correction of plans and forecasts is carried out on the basis of feedback information containing data on the results of the implementation of plans, and forecasts, clarification of needs, changes in the development trend of the object and the external environment (socio-political, scientific, technical and economic background) .

The varying degree of uncertainty of the generated information about the future affects the nature of the applied methods, methods and techniques of forecasting and planning. If in the development of plans, preference is given to deterministic methods, then in forecasting - stochastic. When drawing up plans, regular methods are predominantly used, while forecasting is heuristic.

The specifics of the stages and stages of planning also affect the number and level of aggregation of planned and forecast indicators, the degree of their determinism, the ratio of directive and calculated indicators.

2 METHODS OF SCIENTIFIC AND TECHNICAL FORECASTING

2.1 Classification of forecasting methods

First of all, let us give a definition of the forecasting method as a method of theoretical and practical action aimed at developing forecasts. This definition is quite general and allows us to understand the term "forecasting method" very broadly: from the simplest extrapolation calculations to complex procedures of multi-step expert surveys.

To study the methodological apparatus of forecasting, it is advisable to detail this broad concept from the very beginning. Further, we will distinguish between simple forecasting methods and complex forecasting methods. At the same time, by a simple forecasting method we will understand a method that cannot be decomposed into even simpler forecasting methods, and, accordingly, by a complex method, we mean a method consisting of an interconnected set of several simple ones.

At present, along with a significant number of published forecasting methods, numerous ways of classifying them are known. Nevertheless, this issue cannot be considered satisfactorily resolved, since a single, useful and complete classification has not yet been created. Probably, prognostics, as a young science, has not yet reached such a level of development when it is possible to create a classification that satisfies all these requirements. So, what are the goals of classifying forecasting methods? Two such main goals can be identified. This is, firstly, ensuring the process of studying and analyzing methods and, secondly, servicing the process of choosing a method when developing object forecasts. On the present stage it is difficult to propose a single classification that equally satisfies both of these goals.

There are two main types of classification: sequential and parallel. consistent classification presupposes the isolation of private volumes from more general ones. This is a process identical to the division of a generic concept into specific ones. In this case, the following basic rules must be observed: 1) the basis of division (attribute) must remain the same in the formation of any specific concept; 2) the scope of specific concepts must exclude each other (requirement for the absence of intersection of classes); 3) the scope of specific concepts should exhaust the scope of the generic concept (the requirement for full coverage of all objects of classification).

Parallel classification assumes a complex information basis, consisting not of one, but of a number of features. The basic principle of such a classification is the independence of the selected features, each of which is essential, all together are simultaneously inherent in the subject, and only their combination gives an exhaustive idea of each class.

Sequential classification has a visual interpretation in the form of a genealogical tree, covers the entire area under consideration as a whole and determines the place and relationships of each class in common system. Therefore, it is more acceptable for the purposes of study, allows methodically more harmonious presentation of the classified area of knowledge.

Each level of classification is characterized by its own classification feature. The elements of each level are the names of the subsets of the elements of the nearest lower level that belong to them, and the subsets are disjoint.

The elements of the lower level are the names of narrow groups of specific forecasting methods (sometimes from one element), which are modifications or varieties of any one, the most general of them.

In general, the classification is open, since it represents the possibility of increasing the number of elements at the levels and increasing the number of levels due to further fragmentation and refinement of the elements of the last level.

At the first level, all methods are divided into three classes according to the sign "information basis of the method". Factual methods are based on actually available information material about the object of forecasting and its past development. Expert methods are based on information supplied by expert experts in the process of systematized procedures for identifying and summarizing this opinion. Combined methods are separated into a separate class so that it can be classified as methods with a mixed information base, in which factual and expert information is used as primary information. For example, when conducting an expert survey, participants are presented with digital information about an object or factual forecasts, or, conversely, when extrapolating a trend, along with actual data, expert estimates are used.

Those forecasting methods that apply mathematical processing methods to expert initial information or evaluate the original factual information by expert means should not be classified as combined methods. In most cases, they fit fairly well into the first or second of the above classes.

These classes are further divided into subclasses according to the principles of information processing. Statistical methods combine a set of methods for processing quantitative information about the object of forecasting according to the principle of identifying the mathematical patterns of development contained in it and the mathematical relationships of characteristics in order to obtain predictive models. Analogy Methods are aimed at identifying similarities in the patterns of development of various processes and, on this basis, making forecasts. Leading forecasting methods are based on certain principles of special processing of scientific and technical information, realizing in the forecast its property to outstrip the development of scientific and technical progress.

Expert methods are divided into two subclasses. Direct expert assessments are based on the principle of obtaining and processing an independent generalized opinion of a group of experts (or one of them) in the absence of influence on the opinion of each expert of the opinion of another expert and the opinion of the group. Expert assessments with feedback in one form or another embody the principle of feedback by influencing the assessment of an expert group (one expert) with the opinion previously received from this group or from one of its experts.

The third level of classification divides forecasting methods into types according to the classification feature "apparatus of methods". Each type combines in its composition methods that have the same apparatus for their implementation as a basis. So, statistical methods by type are divided into methods of extrapolation and interpolation; methods using the apparatus of regression and correlation analysis; methods using factor analysis.

The class of analogy methods is subdivided into methods of mathematical and historical analogies. The former use objects of a different physical nature, another field of science, a branch of technology as an analogue for the forecasting object, but having a mathematical description of the development process that coincides with the forecasting object. The latter use processes of the same physical nature as an analogue, which are ahead of the development of the object of forecasting in time.

Leading forecasting methods can be divided into methods for studying the dynamics of scientific and technical information; methods of research and evaluation of the level of technology. In the first case, the construction of quantitative and qualitative dynamic series based on various types of NTI and analysis and forecasting of the corresponding object based on them is mainly used. The second type of methods uses a special apparatus for analyzing the quantitative and qualitative information contained in the NTI to determine the characteristics of the level and quality of existing and designed equipment.

Direct expert assessments on the basis of the implementation apparatus are divided into types of expert survey and expert analysis. In the first case, special procedures are used to form questions, organize the receipt of answers to them, process the received answers and form the final result. In the second, the main apparatus of research is a purposeful analysis of the object of forecasting by an expert or a team of experts who themselves raise and solve questions leading to the goal.

Expert assessments with feedback in their apparatus have three types of methods: expert survey; idea generation; game simulation. The first type is characterized by the procedures of a regulated non-contact survey of experts with intermittent feedback in the sense considered above. The second one is built on the procedures of direct communication between experts in the process of exchanging views on the problem posed. It is characterized by the absence of questions and answers and is aimed at mutual stimulation creative activity experts. The third type uses the apparatus of game theory and its applied sections. As a rule, it is implemented on a combination of dynamic interaction between teams of experts and a computer that imitates the object of forecasting in possible future situations.

Finally, the last, fourth, level of classification subdivides the types of methods of the third level into separate methods and groups of methods according to some local sets of classification features for each type, of which it is impossible to indicate one common for the entire level as a whole.

2.2 Extrapolation forecasting methods

Trend extrapolation methods are perhaps the most common and most developed among the entire set of forecasting methods. The use of extrapolation in forecasting is based on the assumption that the process of changing the variable under consideration is a combination of two components - regular and random:

It is believed that the regular component f(a, X) represents smooth function on the argument (in most cases, time), described by a finite-dimensional vector of parameters a, which retain their values on the forecast lead period. This component is also called trend, level, determined basis of the process, trend. Under all these terms lies an intuitive idea of some kind of essence of the analyzed process cleared of interference. Intuitive, because for most economic, technical, natural processes it is impossible to unambiguously separate the trend from the random component. It all depends on what purpose this division pursues and with what accuracy it is carried out.

Random component n (X) is usually considered to be an uncorrelated random process with zero expectation. Its estimates are necessary for further determination precision forecast characteristics.

Extrapolation forecasting methods focus on highlighting the best description of the trend in some sense and on determining forecast values by extrapolating it. Extrapolation methods largely intersect with forecasting methods based on regression models. Sometimes their differences come down only to differences in terminology, notation, or formula writing. Nevertheless, predictive extrapolation itself has a number of specific features and techniques that allow it to be classified as a certain independent type of forecasting methods.

Specific features of predictive extrapolation include methods for preprocessing a number series in order to convert it to a form convenient for forecasting, as well as an analysis of the logic and physics of the predicted process, which has a significant impact both on the choice of the type of extrapolating function and on determining the boundaries changing its settings.

2.2.1 Pre-processing of initial information in predictive extrapolation problems

Pre-processing of the original number series is aimed at solving the following tasks (all or part of them): reduce the influence of the random component in the original number series, i.e. bring it closer to the trend; present the information contained in the numerical series in such a way as to significantly reduce the difficulty of the mathematical description of the trend. The main methods for solving these problems are the procedures for smoothing and leveling the statistical series.

Procedure smoothing is aimed at minimizing random deviations of the points of the series from some smooth curve of the assumed trend of the process. The most common method of averaging the level over a certain set of surrounding points, and this operation moves along a number of points, in connection with which it is usually called a moving average. In the very simple version the smoothing function is linear and the smoothing group consists of the previous and subsequent points, in more complex ones the function is non-linear and uses a group of an arbitrary number of points.

Smoothing is performed using polynomials that approximate groups of experimental points using the least squares method. The best smoothing is obtained for the middle points of the group, so it is desirable to choose an odd number of points in the group to be smoothed.

Smoothing, even in a simple linear version, is in many cases a very effective means of identifying a trend when superimposed on an empirical numerical series of random noise and measurement errors. For series with a significant noise amplitude, it is possible to carry out multiple smoothing of the original numerical series. The number of successive smoothing cycles should be selected depending on the type of the original series, on the degree of its supposed noise content with interference, and on the goal pursued by smoothing. It must be borne in mind that the effectiveness of this procedure quickly decreases (in most cases), so it is advisable to repeat it from one to three times.

Linear smoothing is a fairly crude procedure that reveals the general approximate form of the trend. To more accurately determine the shape of the smoothed curve, a non-linear smoothing operation or weighted moving averages can be used. In this case, the ordinates of the points included in the sliding group are assigned different weights depending on their distance from the middle of the smoothing interval.

If smoothing is aimed at the primary processing of a number series to eliminate random fluctuations and identify a trend, then alignment serves the purpose of a more convenient presentation of the original series, leaving its values unchanged.

The most common leveling techniques are logarithm and change of variables.

If the empirical formula is assumed to contain three parameters or it is known that the function is three-parameter, sometimes it is possible to exclude one of the parameters by some transformations, and the remaining two lead to one of the alignment formulas.

Alignment can be considered not only as a method of representing the initial data, but also as a method of direct approximate determination of the parameters of a function that approximates the original numerical series. This is often how this method is used in some extrapolation forecasts. Note that the possibility of its direct use to determine the parameters of the approximating function is determined mainly by the type of the original numerical series and the degree of our knowledge, our confidence regarding the type of function that describes the process under study.

In the event that the type of function is unknown to us, alignment should be considered as a preliminary procedure, during which, by applying various formulas and techniques, the most suitable look function describing the empirical series.

One of the varieties of the alignment method is the study of an empirical series in order to clarify some properties of the function that describes it. In this case, transformations do not necessarily lead to linear forms. However, the results prepare them and facilitate the process of choosing an approximating function in prognostic extrapolation problems. In the simplest case, it is proposed to use the following three types of differential growth functions:

1) First derivative, or absolute differential growth function.

2) Relative differential coefficient, or logarithmic derivative,

3) Elasticity of function

2.3 Statistical methods

Before proceeding to the analysis of statistical forecasting methods, we consider some general concepts and definitions related to correlation and regression models. Two random variables are correlated if expected value one of them changes depending on the change of the other.

Application correlation analysis involves the fulfillment of the following prerequisites:

a) Random variables y(y 1 , y 2 , ..., U n) and x(x 1 , x 2 , ..., X n) can be viewed as a sample from a two-dimensional population with normal law distribution.

b) Expected error and zero

c) Individual observations are stochastically independent, that is, the value of a given observation should not depend on the value of the previous and subsequent observations.

d) Covariance between the error associated with one value of the dependent variable y, and the error associated with any other value of y is zero.

e) Variance of error associated with a single value y, equals the variance of the error associated with any other value.

f) The covariance between the error and each of the independent variables is zero.

g) The direct applicability of this method is limited to cases where the equation of the curve is linear with respect to its parameters b o , b i , ...,b k This, however, does not mean that the equation of the curve itself with respect to the variables must be linear. If the empirical equations of observation are not linear, then in many cases it is possible to reduce them to a linear form and already . then apply the least squares method.

h) Observations of independent variables are made without error.

Before starting the correlation analysis, it is necessary to check the fulfillment of these prerequisites.

The relationship between random and non-random variables is called regression, and the method of analyzing such relationships is regression analysis. The use of regression analysis presupposes the obligatory fulfillment of the prerequisites (b-d) of the correlation analysis. Only if the above prerequisites are met, the estimates of the correlation and regression coefficients obtained using the least squares method will be unbiased and have a minimum variance.

Regression analysis is closely related to correlation analysis. When the prerequisites of the correlation analysis are met, the prerequisites of the regression analysis are fulfilled. At the same time, regression analysis imposes less stringent requirements on the initial information.” So, for example, regression analysis is possible even if the distribution of a random variable differs from a normal one, as is often the case for technical and economic variables. A random variable is used as a dependent variable in a regression analysis, and a non-random variable is used as an independent variable.

According to the degree of complexity, statistical studies can be divided into two-dimensional and multidimensional. The first relate to the consideration of paired relationships between variables (paired correlations and regressions) and are aimed in predictive studies at solving such problems as establishing a quantitative measure of the tightness of the relationship between two random variables, establishing the proximity of this relationship to a linear one, assessing the reliability and accuracy of forecasts obtained by extrapolation of the regression dependence. Multidimensional methods of statistical - analysis are mainly aimed at solving the problem of system analysis of multidimensional stochastic forecasting objects. The purpose of such an analysis is, as a rule, the clarification of internal relationships between the variables of the complex, the construction of multidimensional functions of the connection of variables, the selection of the minimum number of characteristics that describe the object with a sufficient degree of accuracy. One of the main tasks here is to reduce the dimension of the description of the forecasting object.

Thus, statistical methods are mainly used to prepare data, bringing them to a form suitable for making a forecast. As a rule, after their application, one of the methods of extrapolation or interpolation is used to obtain a directly predictive result.

2.4 Expert methods

2.4.1 Scope of expert methods

Methods of expert assessments in forecasting and long-term planning of scientific and technological progress are used in the following cases:

a) in the absence of sufficiently representative and reliable statistics on the characteristics of the object (for example, lasers, holographic storage devices, rational use of water resources in enterprises);

b) under conditions of great uncertainty in the environment for the operation of an object (for example, forecasts of a man-machine system in space or taking into account the mutual influence of the fields of science and technology);

c) in medium- and long-term forecasting of objects of new industries that are strongly influenced by new discoveries in the fundamental sciences (for example, the microbiological industry, quantum electronics, nuclear engineering);

d) in conditions of lack of time or extreme situations.

An expert assessment is necessary when there is no proper theoretical basis for the development of an object. The degree of reliability of expertise is established by the absolute frequency with which the expert's assessment is ultimately confirmed by subsequent events. There are two categories of experts - these are narrow specialists and generalists who provide the formulation of major problems and the construction of models. The choice of experts for the forecast is made on the basis of their reputation among a certain category of specialists. However, one should not forget the circumstance that a first-class specialist cannot always adequately consider and understand general, global issues. For this purpose, it is necessary to involve experts, although not narrowly informed, but possessing the ability to be daring and imaginative.

"Expert" in literal translation from Latin means "experienced". Therefore, both in the formalized and non-formalized methods of determining an expert, professional experience and intuition developed on its basis occupy a significant place. The conditions for the necessity and sufficiency of referring a specialist to the category of experts are introduced as follows.

It is important to establish not the absolute degree of reliability of the expert assessment, but the degree of reliability in comparison with the assessment of the average specialist, as well as the correlation between the probability of his predictive assessment and the reliability of the class of hypotheses that the expert operates with. In general, you need to define what an expert is. Here are some of the requirements that an expert must meet:

1) expert estimates must be stable in time and transitive; 2) the availability of additional information about the predicted signs only improves the assessment of the expert; 3) the expert must be a recognized specialist in this field of knowledge; 4) the expert must have some experience of successful forecasts in the given field of knowledge.

When characterizing experts, it should be borne in mind that two types of errors may occur as a result of the development of estimates. Errors of the first type are known in measurement technology as systematic, errors of the second type as random. An EA that is prone to errors of the first type produces values that steadily differ from the true one in the direction of increasing or decreasing. Errors of this kind are believed to be due to the mentality of the experts. To correct systematic errors, you can apply correction factors or use specially designed training games. Errors of the second type are characterized by the magnitude of the dispersion. Based on the analysis of the main types of errors in making expert judgments, one more thing can be added to the list of requirements for experts considered earlier. Its meaning is that one should prefer an expert, whose estimates have a small variance and a systematic deviation of the mean error from zero, to an expert with a mean error equal to zero, but with a larger variance. Unfortunately, it is impossible to determine a priori a person's ability to make correct expert assessments. An important means of preparing experts are special training games.

The organization of the expert’s work forms can be programmed or non-programmed, and the expert’s activities can be carried out orally (interviews) or in writing (answering questions from special tables of expert assessments or a free presentation on a given topic).

Programming the form of work of an Expert Advisor involves:

building a graph model of an object based on a retrospective analysis; determination of the structure of the tables of expert assessments (feasibility study) or the interview program based on the graph model of the object and the objectives of the examination; determining the type and form of questions in a feasibility study or in an interview;

determining the type of scale for questions in the feasibility study; taking into account the psychological characteristics of the examination in determining the sequence of questions in the feasibility study; accounting for verification questions; development of logical methods for the subsequent synthesis of predictive estimates in complex forecasts of the object.

The organization of stimulation of the work of an expert consists in the development of:

heuristic techniques and methods that facilitate the search for a predictive expert assessment; legal norms that guarantee the expert registration of priority and authorship, as well as non-disclosure of all scientific and technical ideas put forward by him in the process of examination;

forms of moral, professional and material interest of an expert in expert assessments; organizational forms of the expert's work (inclusion in the work plan, etc.).

Based on the model of the forecasting object obtained as a result of the analysis, the scientific and technical areas in which it is necessary to involve an expert are determined, groups of experts are distinguished according to whether the issue belongs to the field of fundamental, applied sciences or to joint scientific areas.

When solving the problem of forming an expert group, it is necessary to identify and stabilize an efficient network of experts. The way to stabilize the expert network is as follows. Based on the analysis of the literature on the predicted problem, any specialist with several publications in this field is selected. He is asked to name the 10 most competent, in his opinion, experts on this problem. Then they turn simultaneously to each of the ten named specialists with a request to indicate the 10 most prominent of their fellow scientists. From the list of specialists received, 10 initial ones are deleted, and letters containing the above request are sent to the rest. This procedure is repeated until none of the newly named specialists adds new names to the list of experts, i.e. until the network of experts stabilizes. The resulting network of experts can be considered a general set of specialists who are competent in the field of the predicted problem. However, due to a number of practical limitations, it turns out to be inappropriate to involve all specialists in the examination. Therefore, it is necessary to form a representative sample from the general population of experts.

The determination of the specifics of procedures for methods of the PEO class (personal expert assessments) is carried out on the basis of an analysis of the requirements for experts and their assessments arising from the essence of the methods:

a) analytical notes require the structuring of the experimental problem, the explication and ranking of goals, the analysis of alternative ways to achieve the goal, the cost estimate for each alternative, and recommendations for the most effective ways problem solution;

b) pairwise comparisons, normalization and ranking require the homogeneity of the evaluated features, the presence of logically justified criteria and standards, the existence of unambiguously defined procedures for operating with criteria, standards and features;

c) interview impose specific requirements on both the expert and the interviewer;

d) morphological structuring requires a clear definition of the functional characteristics of the object or problem that needs to be improved, the classification of scientific principles, on the basis of which it is possible to improve the characteristics; analysis of all possible combinations of these principles and elimination of obviously absurd ones; assessment of combinations according to the degree of feasibility and the cost of their implementation; comparison of combinations according to the complex criterion "costs - efficiency - time".

2.4.2 Heuristic forecasting method (HEP)

The main task facing specialists in analysis and design large systems, in the general case, as a rule, is to find the most optimal ways to create more efficient systems - either newly designed or modernized. The complexity of solving this problem lies primarily in the fact that here it is usually not possible to find a solution using purely mathematical methods, since, as a rule, it is not possible to accurately determine the quantities (functionals) that are subject to optimization (extremalization) in the mathematical sense. This is due not only to the complexity of describing the functioning of large systems, but also to such fundamental types as, for example, the specific goals for which the system is intended. First, the system may have not one goal, but a set of them, which immediately leads to a vector optimization problem. Secondly, the set of goals set for the system may contain purely qualitative goals that are not subject to practical quantitative measurements. This leads, on the one hand, to the problem of assessing the degree of achievement of a qualitative goal and, on the other hand, to the problem of measuring the importance of qualitative and quantitative goals and the degree of their achievement.

A similar situation arises when assessing the consequences of the proposed method of achieving the goal. Let us point out, for example, that these consequences can simultaneously be economic, political, social or any other nature.

Under these conditions, the solution of the system problem is found through heuristic techniques that use a very complex mathematical apparatus, and consists in issuing reasonable recommendations sufficient to develop a solution.

The method of heuristic forecasting is the method of obtaining and specialized processing of predictive estimates of an object through a systematic survey of highly qualified specialists (experts) in a narrow field of science, technology or production. Forecast expert assessments reflect the individual judgment of a specialist regarding the prospects for the development of his field and are based on the mobilization of professional experience and intuition.

The heuristic forecasting method is similar to the Delphi technique, collective idea generation and the method of collective expert evaluation in the sense that one of its elements is the collection and processing of expert judgments expressed on the basis of professional experience and intuition. However, it differs from these methods in greater clarity. theoretical foundations, methods of forming questionnaires and tables, the procedure for working with experts and the algorithm for processing the information received. This method is called heuristic due to the homogeneity of the forms of the expert's mental activity in solving a scientific problem and in assessing the prospects for the development of the object of forecasting, as well as in connection with the use by experts of specific techniques that lead to plausible conclusions.

The purpose of the heuristic forecasting method is to identify an objectified idea of the development prospects for a narrow field of science and technology based on a systematic processing of forecast estimates from a representative group of experts.

The scope of the MEP is scientific and technical objects and problems, the development of which either completely or partially cannot be formalized, i.e., for which it is difficult to develop an adequate model. For example, the element-technological base of the digital computer.

The method is based on three theoretical assumptions: 1) the existence of an expert's psychological attitude to the future, formulated on the basis of professional experience and intuition, and the possibility of its exteriorization; 2) the identity of the process of heuristic forecasting and the process of solving a scientific problem with the uniformity of the knowledge obtained in the form of heuristic plausible conclusions that require verification;

3) the possibility of adequately displaying the development trend of the forecasting object in the form of a system of forecasting models synthesized from forecasting expert assessments.

These assumptions are implemented in the heuristic forecasting method through a system of methods of working with experts, methods of estimation and synthesis of predictive models.

The source documents when working on the heuristic forecasting method are: description of the method; instructions for formulating questions; instructions for compiling questionnaires and tables of expert assessments; procedure for working with experts; a set of heuristic techniques for experts; instructions for experts on filling out questionnaires and tables; instruction for computer processing of expert questionnaires and tables; algorithms and programs for data processing on a computer; questionnaires and tables filled in by experts; instructions for evaluating the competence of experts; instructions for synthesizing predictive models; a set of methods for verifying forecasts.

The presence of a fully formulated information array gives a full basis for high-quality work with the MEP.

Formation of questionnaires and tables of expert assessments. The information array for developing forecasts using the heuristic forecasting method is a set of tables and questionnaires filled in by experts. The tables contain a list of strictly formulated questions. The following requirements are imposed on the questions in the questionnaires: 1) they must be formulated in generally accepted terms; 2) their formulation should exclude any semantic ambiguity; 3) all questions must logically correspond to the structure of the forecast object; 4) they must be assigned to one of the three types listed below. Depending on the type of question, a certain procedure for its formulation and compilation of questionnaires is applied.

To first type includes questions, the answers to which contain a quantitative assessment: questions regarding the time of the occurrence of events; surveys regarding the quantitative value of the predicted parameter; questions regarding the likelihood of an event occurring; questions on assessing the relative influence of factors on each other in a certain scale. For this type of question, the simplest procedure for compiling questionnaires is used. In this case, the forecaster himself, who knows the object of the forecast, formulates a list of values of the estimated parameters, probabilities and time intervals. When determining the scale of values of quantitative parameters (time, characteristics, etc.), it is advisable to use an uneven scale. The specific value of unevenness is determined by the nature of the dependence of the forecast error on the lead time.

Co. second type include substantive questions that require a concise answer not in a quantitative form. Questions requiring an answer in a folded form can be of three types: disjunctive; conjunctival; implicative.

Questions that require a meaningful answer in a folded form are characterized by the most complex procedure for their formation into a questionnaire. The questionnaire in its final form is obtained as a result of a three-stage iteration. At the first stage, the forecaster carefully studies the result of the work (report) of a group of experts (method of commissions) on a particular system. The result of the study is the formulation of the first version of the questionnaire, which at the second stage is sent to the chairmen of the relevant commissions for correction and clarification. The result is the second version of the questionnaire. At the third stage, questions are grouped by topics and in a certain order within the topics. The final version of the questionnaire takes the form of tables of expert assessments.

Classification and review of basic forecasting methods. Methods of financial forecasting

Types of forecasts

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