Classification of methods and models of forecasting. Application of information technologies in economic and mathematical forecasting

The need for forecasting is objective. The future of many phenomena is unknown, but it is very important for the decisions made at the moment.

The need for forecasting is objective. The future of many phenomena is unknown, but it is very important for the decisions made at the moment. The processes that urgently require the use of forecasting procedures include economic activity. However, all stages of forecasting, including its organization, provision and interpretation of the results, are far from trivial. And IT can help a lot.

Forecasting: successes and failures

To date, a lot of research has been carried out and impressive results have been obtained. practical solutions forecasting problems in science, technology, economics, demography and other areas. Attention to this problem is due, among other things, to the scale of the modern economy, the needs of production, the dynamics of the development of society, the need to improve planning at all levels of management, as well as the accumulated experience. Forecasting is one of the decisive elements effective organization management of individual business entities and economic communities due to the fact that the quality of decisions made is largely determined by the quality of predicting their consequences. Therefore, decisions made today should be based on reliable estimates of the possible development of the studied phenomena and events in the future.

The improvement of forecasting by many experts is seen in the development of appropriate information technologies. The need for their use is due to a number of reasons, including:

• growth of volumes of information;
• the complexity of the algorithms for calculating and interpreting the results;
• high requirements for the quality of forecasts;
• the need to use forecasting results to solve planning and control problems.

From time to time there is information about the positive results achieved by a particular company. A number of publications note that a successful assessment of trends in the market situation, demand for goods or services, as well as other economic processes and characteristics allows you to get a significant increase in profits, improve other economic indicators. The mechanism of success at first glance is simple and clear: assuming what will happen in the future, effective measures can be taken in a timely manner, using positive trends and compensating for negative processes and phenomena.

However, there are also negative examples. As CIO magazine previously noted, Cisco, once hailed as a symbol of the new economy, not only failed to foresee the 2001 economic downturn, but was even worse off than others because it considered its software and methodological demand forecasting impeccable. The company's management did not assume that one of the reasons for its crisis could be the forecasting methods and technologies used. As a result of an analytical error, $2.2 billion worth of goods was written off, about 20% of employees were fired, and the company's shares fell almost six times in price. Thus, the cause of the Cisco crisis does not lie in the delays in obtaining or the insufficient amount of initial information necessary for the work of the company's analysts. Difficulties arose, obviously, due to methodological errors and inadequate evaluation of the received forecasts. It can be assumed that the model used by Cisco did not provide the necessary level of adaptation of forecast estimates to the current change in the market situation.

Ensuring the quality of forecasting

Accuracy, reliability and efficiency, however, as well as other components of the quality of forecasting, are provided by a number of factors, among which it is necessary to highlight:

• software, which is based on economic and mathematical models adequate to reality; n completeness of coverage and reliability of sources of initial information on which the work of forecasting algorithms is based;
• Efficiency of processing internal and external information;
• the ability to critically analyze forecast estimates;
• the timeliness of making the necessary changes in the methodological and informational support of forecasting.

Special software is based on carefully selected models, methods and techniques. Their implementation is extremely important for obtaining high-quality forecasts when solving problems of the current and strategic planning. An analysis of the current situation shows that the difficulties in introducing IT, which provide forecasting of economic processes, are not only technical or methodological, but also organizational and psychological in nature. Consumers of the results sometimes do not understand the principles of the models used, their formalization and objectively existing limitations. This, as a rule, gives rise to distrust of the results obtained. Another group of implementation problems is related to the fact that predictive models are often closed, autonomous, and therefore their generalization for the purpose of development and mutual adaptation is difficult. Hence, compromise solution it may turn out to be a step-by-step approach with the highlighting of the main analytical tasks.

However, there are practically no ready-made replicated or corporate solutions that provide forecasting for small and medium-sized economic entities at the system level with high quality and affordable prices. Currently automated systems enterprise management are limited mainly to elementary tasks of accounting and control. The reason for this situation is that before the advent of modern IT there were no wide opportunities to use effective economic and mathematical models directly in the process of economic activity. In addition, the use of existing forecasting models for analytical purposes did not put forward such high requirements for their information support.

Fundamentals of forecasting technologies

When building a predictive system from scratch, it is necessary to resolve a number of organizational and methodological issues. The first ones include:

• user training in methods of analysis and interpretation of forecast results;
• determining the directions of movement of predictive information within the enterprise, at the level of its divisions and individual employees, as well as the structure of communications with business partners and authorities;
• determining the timing and frequency of forecasting procedures;
• development of principles for linking the forecast with forward planning and the procedure for selecting options for the results obtained when drawing up an enterprise development plan.

The methodological problems of building a forecasting subsystem are:

• development internal structure and the mechanism of its functioning;
• organization of information support;
• development of mathematical software.

The first problem is the most difficult, since to solve it it is necessary to build a set of forecasting models, the scope of which is a system of interrelated indicators. The problem of systematization and evaluation of forecasting methods appears here as one of the central ones, since in order to select a specific method, it is necessary to conduct them. comparative analysis. A variant of the classification of forecasting methods, taking into account the peculiarities of the knowledge system that underlies each group, can be summarized as follows: methods of expert assessments; methods of logical modeling; mathematical methods.

Each group is suitable for solving a certain range of tasks. Therefore, practice puts forward the following requirements for the methods used: they must be focused on a specific forecasting object, must be based on a quantitative measure of adequacy, and be differentiated in terms of the accuracy of estimates and the forecasting horizon.

The main tasks that arise in the process of creating a predictive system are divided into:

• building a system of predictable processes and indicators;
• development of an apparatus for economic and mathematical analysis of predicted processes and indicators;
• concretization of the method of expert assessments, selection of indicators for examination and obtaining expert assessments of some predicted processes and indicators;
• forecasting indicators and processes indicating confidence intervals and accuracy;
• development of methods for interpreting and analyzing the results obtained.

The work on the information and mathematical support of the forecasting system deserves special attention. The process of creating software can be represented as the following steps:

1. development of a method for structural identification of the object of forecasting;
2. development of methods for parametric identification of the forecasting object;
3. development of methods for predicting trends;
4. development of methods for predicting the harmonic components of processes;
5. development of methods for assessing the characteristics of random components of processes;
6. creation of complex models for predicting indicators that form an interconnected system.

The creation of a forecasting system requires an integrated approach to solving the problem of its information support, which is usually understood as a set of initial data used to obtain forecasts, as well as methods, methods and tools that ensure the collection, accumulation, storage, search and transmission of data in the process of functioning of the forecasting system. and its interaction with other enterprise management systems.

Information support of the system usually includes:

Information fund (database);

Sources of formation of the information fund, flows and methods of data receipt;

Methods of accumulation, storage, updating and retrieval of data that form the information fund;

Methods, principles and rules of data circulation in the system;

Methods for ensuring the reliability of data at all stages of their collection and processing;

Methods information analysis and synthesis;

Methods for an unambiguous formalized description of economic data.

Thus, the following main components are required to implement the forecasting process:

Sources of internal information, which is based on management and accounting systems;

Sources of external information;

Specialized software that implements forecasting algorithms and analysis of results.

In addition to these components, appropriate technologies for storing, exchanging and presenting information should be used.

Forecast Quality Confirmation

Given the importance of solving the problem of forecasting for market participants, it is advisable to check the quality of the proposed methods and algorithms, as well as technologies in general, using specially selected (test) initial data. A similar verification method has been used for a long time in assessing the adequacy of mathematical tools designed for nonlinear optimization, for example, using the Rosenbrock and Powell functions.

Confirmation (or verification) of the quality and performance of the forecasting technology is usually carried out by comparing a priori known model data with their predicted values ​​and evaluating the statistical characteristics of forecast accuracy. Let's consider this trick in a situation where the process models are an additive set of the trend Tt, seasonal (harmonic) and random components.

On fig. 1, as an illustration of the trend of the additive model, a second-order parabolic trend is presented, in fig. 2 - seasonal component of the process with a period of 12 months, and in fig. 3 - random component. A comparison of the actual implementation of the process with its forecast, carried out within the framework of the methodology of short-term forecasting, is shown in Fig. 4. Absolute errors are illustrated in fig. 5. The quality of technology is assessed by the statistical characteristics of errors in forecast estimates.

Practice and prospects for the development of forecasting in replicated and corporate systems

At present, a wide variety of software tools have become widespread, providing, to one degree or another, the collection and analytical processing of information. Some of them, such as MS Excel, are equipped with built-in statistical functions and programming tools. Others, especially inexpensive accounting and management accounting programs, do not have such capabilities or analytical capabilities are not implemented in them sufficiently, and sometimes incorrectly. However, this is unfortunately inherent in some more powerful and multifunctional enterprise management systems, which was confirmed at the past exhibitions "Apteka 2001" (November-December 2001) and "Accounting and Auditing 2002" (January 2002). This situation is apparently explained by a shallow analysis on the part of the developers of the properties of the forecasting algorithms they have chosen and their uncritical application. For example, judging by available sources, zero-order exponential smoothing is often used as the basis of predictive algorithms. However, this approach is valid only if there is no trend in the process under study. In fact, economic processes are non-stationary, and forecasting involves the use of more complex models than models with a constant trend.

It is interesting to trace the path of development of domestic automated banking systems from the perspective of the topic under consideration. The first banking systems were based on rigid technology, constantly requiring changes or additional software. This prompted developers of financial software, following the principles of openness, scalability and flexibility, to use industrial DBMS. However, by themselves, these DBMS turned out to be unsuitable for solving high-level analytical problems, which include the problem of forecasting. To do this, it was necessary to use additional technologies for data storage and operational analytical processing, which ensured the operation of decision support systems for financial and credit institutions and for making forecasts. The same approach is used in complex enterprise management systems.

Another direction of modern applied use of forecasting methods based on IT is the solution of a wide range of marketing tasks. An illustration is the SAS Churn Management Solution for Telecommunications software. It is intended for telecommunications operators and allows, as its developers claim, to build predictive models and use them to assess the likelihood of an outflow of certain categories of customers. The basis of this software is the Scalable Performance Data Server distributed database server, tools for building and administering data warehouses and data marts, Enterprise Miner data mining toolkit, SAS / MDDB Server decision support system, as well as aids. To ensure the competitiveness of newfangled CRM-systems in the list of their advanced features, as well as for automated banking systems, reporting functions are included that use OLAP technologies and allow, to a certain extent, to predict the results of marketing, sales and customer service.

There are quite a lot of specialized software products that provide statistical processing of numerical data, including individual elements of forecasting. These products include SPSS, Statistica, etc. These tools have both advantages and disadvantages that significantly limit their scope. practical application. It should be noted here that the assessment of the suitability of specialized mathematical and statistical software tools for solving forecasting problems by ordinary users who do not have special training requires a separate serious study and discussion.

However, solving forecasting problems for consumers from small and medium-sized businesses with the help of powerful and expensive information systems and technologies is practically impossible, primarily for financial reasons. Therefore, a very promising direction is the development of the analytical capabilities of existing and widespread low-cost accounting and management accounting systems. Developed additional reports based on specific business processes and containing the necessary analytical information for a particular user have a high ratio of "efficiency - cost".

Some software developers create entire lines of analytical tools. For example, Parus Corporation offers Parus-Analytics and Triumph-Analytics solutions for a wide range of users from small and medium-sized businesses. More complex tasks of analytical processing of forecast information are integrated into the Parus system in the form of a so-called situational center. According to Dmitry Sudarev, circulation solutions development manager, in 1997 it was decided to develop and implement software products, allowing you to move from a simple accounting of facts in the activities of the enterprise to the analysis of information. At the same time, a transition was planned from automating the work of accountants and middle managers to processing information for top management. Taking into account the possible circle of consumers, Parus-Analytics and Triumph-Analytics do not impose special requirements on the software and hardware environment, however, the Triumph-Analytics solution is implemented on the basis of MS SQL Server, which provides it with greater opportunities for predicting the processes under study , in particular, the harmonic component of forecasts is taken into account.

The value of the forecast increases many times when it is directly used in the management of the enterprise. Therefore, an important direction is the integration of predictive systems with systems such as Kasatka, MS Project Expert, etc. For example, the Kasatka software from SBI is positioned as an automated workplace head and specialists of the marketing department and is intended for the development of complexes of management, marketing and strategic planning. Such a purpose predetermines the need to identify long-term trends and take them into account in planning. The forecasting horizon is determined based on the relevant goals of the organization.

Conclusion

The choice of forecasting technology and means of its implementation should be carried out in accordance with the goals and objectives of a particular consumer, take into account the level of information support, the qualifications of users and a number of other factors. These reasons require individual development or adaptation of previously created special software.

Literature

Glossary

Forecasting(in economic planning) - the scientific and analytical stage of the economic planning process. The main tasks of forecasting in the development of economic plans are: scientific analysis of social, economic and scientific and technical processes and trends, objective relationships of socio-economic phenomena in specific conditions, assessment of the current situation and identification of key problems of economic development; assessment of the development of these trends in the future and foreseeing new economic situations, new problems that need to be resolved; identifying possible development alternatives for a reasonable choice of one or another opportunity and making the best decision.

Control automation- the use of methods and techniques of automatic processing of information by the management bodies of the enterprise, including for the development of optimal economic decisions. Management automation is associated with the introduction of economic and mathematical methods and IT.

Information support of the system- a set of methods and means for selecting, classifying, storing, searching, updating and processing information in the system. Information support includes: composition of information (list of information units or aggregates); the structure of information and the patterns of its transformation; characteristics of the movement of information; information quality characteristics; ways of processing information. Information support can be characterized in functional, structural, transformational and organizational and methodological aspects. The objects of the transformational aspect are the transformation of the language economic management by levels and stages of information advancement in the system .

Lag lag- the time interval between the moment of occurrence of the reaction of the system (effect) to the action applied to it and the moment of its application. In socio-economic systems, lag values ​​play a significant role in planning and management. Investment return lags are especially important.

trend(deterministic basis of the predicted process) - the general, main trend in the change in the dynamic series (process) over a sufficiently long period of observation of it. It is generally accepted that the trend is determined by the action of permanent factors.

Harmonic component of the predicted process- component, the action of which is determined by factors of a periodic nature. A special case is the seasonal component, which is determined mainly by climatic conditions and social traditions.

Random component of the predicted process- deviations of the actual values ​​of the process from the predicted ones, the reasons for which have not been established and cannot be identified within the framework of the adopted model.

Economic and mathematical methods- conditional name of a complex of scientific and applied disciplines at the intersection of economics and mathematics. They include the following groups of disciplines: economic and statistical methods; econometrics; research of operations in the economy; economic cybernetics.

Expert assessments- evaluation of processes or phenomena that cannot be directly measured. Expert assessments play a significant role in decision making, including the prediction of alternatives and their consequences.

Heuristic forecasting method- using the opinion of experts in the field; is used to predict processes that cannot be formalized by the time of forecasting. It is synonymous with the peer review method.

Mathematical forecasting methods conditionally subdivided into methods of modeling development processes and methods of extrapolation. They are based on mathematical tools.

Methods of logical forecasting and analysis connected primarily with the analysis of the consistency of the course and results of forecasting. Serve as feedback in the predictive system. The methods of logical analysis, in addition, allow solving independent problems, for example, building morphological models, which are later used as the basis of formalized (mathematical) forecasting models.

Combined forecasting methods- joint use of methods of heuristic and mathematical forecasting in order to combine their inherent advantages and compensate for their shortcomings.

Interval forecast- the range of values ​​in which the predicted value will fall with a given probability with known process parameters .

Forecast quality criteria- the main criterion of quality is the accuracy of the forecast. In addition, criteria for promptness, reliability, etc. can be used.

Forecast errors- the difference between the current observation of the forecasting object and the expected value. Forecasting errors are caused by various reasons: the uncertainty of the future situation; changes in the forecasting object itself; the impact of newly emerging factors, etc. .

Prediction- a judgment about the future state of an object, which is mostly subjective.

Prediction object model- the use of the phenomenon of isomorphism (analogy) to describe the real forecasting object using mathematical relationships and logical conclusions (in more rare cases, physical models are used). The model is some kind of abstraction from reality, taking into account only those characteristics of the original that are of interest or have a significant impact on its development. The difficulty of choosing a forecasting object model is determined by a number of factors: information about processes or objects similar to the one being predicted; accuracy of information about this process(object); the amount of this information. Currently, there are many classifications of forecasting models.

Predictive system- a set of methods, methods and means of collecting initial data, processing information and presenting forecasts with the required quality.

Sources

A study was made of the main directions and problems of implementation in practical activities organizations of modern information and communication technologies. The problems and directions of creating a unified information space. The analysis of the conditions and prerequisites for practical modeling is carried out, the features of the phased construction of predictive models of the activities of organizations are analyzed. Dana a brief description of features of the use of various forecasting models, emphasis is placed on the importance of checking the adequacy of forecasting models. A review of modern information and analytical technologies for forecasting the activities of organizations has been made. Recommendations are given on the use in practice of the results of forecasting the key indicators of the organization.

information and analytical technologies

activity modeling

model adequacy analysis

forecasting the organization's activities

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In the context of the introduction of economic sanctions, a number of Russian enterprises are looking for effective ways to ensure the competitiveness of their products and improve the efficiency of the organization. In difficult economic conditions, it is necessary to use not only practical experience in organizing a business in a certain field of activity, but also modern approaches to business planning. The widespread introduction of information and analytical technologies for modeling and forecasting key business indicators into the practice of activities allows for operational monitoring of business results and the formation of an organization's development strategy. The use of information and analytical technologies allows you to create integrated business results management systems, optimize material and financial flows, minimize the costs of financial and economic activities, maximize the company's profits and solve a number of other tasks.

The processes of informatization of modern society and the processes of implementation of information and communication technologies in all areas of business that are closely related to them are characterized by the massive spread of information and analytical technologies for analyzing the activities of organizations. various areas and forms of ownership. Modern information technologies make it possible to automate a number of the following areas: studying the properties of a system (object), monitoring the dynamics of development of key indicators in all areas of business, optimizing the parameters of the functioning system, creating integrated systems for monitoring and managing the system, planning and forecasting the prospects for the development of the organization.

The strategic goal of introducing information and communication technologies in all spheres of activity of modern society is to create a single information space designed to solve a wide range of issues related to access to unified databases, the prompt provision of statistical reporting, and the creation of integrated monitoring systems for various activities. All this contributes to the creation of fundamentally new opportunities for the development of cognitive creative activity of a person: research, organizational and managerial, expert, entrepreneurial, etc. The creation of a single information space helps to increase the efficiency and quality of monitoring the activities of organizations, intensify scientific research in various areas, reduce the processing time and provide information, the efficiency and effectiveness of system management, the integration of the national information system into international systems of access to information resources in the field of science, culture, business and other areas of activity.

The introduction of information and communication technologies into the practical activities of organizations is characterized by a number of areas and problems:

● The technical equipment of organizations with means of information and communication technologies implies access to modern software and is constrained by organizational and economic factors. So access to "small informatization" is in some cases ineffective, and to "big" - expensive and does not give a quick return.

● The training of specialists in the field of information and communication technologies, especially in the field of network technologies, should become a priority task, on the solution of which the effectiveness of the organization's activities in this direction depends. A highly skilled IT professional can sometimes do the workload of an entire department of an organization. In this regard, it is necessary to increasingly introduce disciplines related to information technology into the activities of educational organizations and increase their practical orientation. Modern system education should focus on the fundamentalization of education at all its levels, the widespread use of innovative education methods and technologies, improving the quality and accessibility of education through the development of a system distance education and equipping the educational process with modern information and communication technologies.

● Creation information bases data in all areas of the organization's activities requires some effort, but is an important link in the integration of the organization's information technologies into a single information space.

One of the topical areas for introducing information and analytical technologies into the practical activities of organizations is the operational monitoring of key business indicators and forecasting alternative options for the development of the company. In the general case, the following sequence of stages in predicting the development of a research system (object) can be distinguished.

● Setting goals and objectives of the study determines the strategic guidelines and tactical directions in the study of the system, which in the course of the study can be refined and concretized.

● The formulation of the conceptual model of the system involves the examination of the system in order to identify its properties, features of dynamics and interrelationships with factors of the external and internal environment. The collection of statistical information about the characteristics of the system involves the further formulation of a verbal descriptive model of the system, which is subject to clarification and formalization. The formulation of the conceptual model of the system involves a list of key questions formulated in terms of a given area of ​​study that meet the objectives of the study, and a set of hypotheses regarding the properties and characteristics of the modeling object.

● Formalization of a verbal descriptive model implies the construction of a mathematical model and the numerical determination of its parameters. An important point at the same time is right choice methods for determining the parameters of the mathematical model. Each system has its own characteristics of development, and such a characteristic of the model as adequacy, i.e. correspondence of the formalized model to the features of real processes that characterize the dynamics of the research system. Depending on the specifics of the research system, various classes of forecasting models can be preliminarily selected, for example, growth curves that characterize the dynamics of the system over time, econometric models that establish and evaluate the relationship between various internal characteristics of the system and a number of external factors, varieties of adaptive models used for highly dynamic systems with seasonal and cyclical fluctuations, from the simplest to autoregressive models with autocorrelated and heteroscedastic residuals.

● Obtaining and interpreting simulation results involve checking a number of properties of the mathematical model, in particular, checking the adequacy and accuracy of the model. The adequacy of the model characterizes the degree of closeness of the characteristics of the constructed model to the characteristics and properties of a real object (system). For a number of reasons, such as a number of assumptions that take place in modeling, the impossibility of taking into account many factors that determine the dynamics of the development of the object of study, a number of technical errors at the stage of model formalization and a number of other points, naturally lead to a difference in the characteristics of the model and the real object . It is important that these differences are not of a fundamental nature and are within certain limits (deviations). The value of permissible deviations is determined by the characteristics of the dynamics of the research system, the period of analysis of the characteristics of the system, as well as the purpose of the study. Model accuracy indicators, such as the standard deviation of a series of residuals, the average approximation error, the average relative error, characterize the degree of approximation of the simulated data to the actual observations obtained as a result of collecting statistical information. At this stage, the refinement and final choice of the model used in the future to build the forecast is carried out. At the same time, an extended verification of the adequacy of the model is carried out, including, in addition to testing hypotheses about the fulfillment of a number of statistical properties of the residual component, such as independence, randomness, the equality of the mathematical expectation of the residuals to zero, the fulfillment of the normal distribution law, the evaluation of a number of such characteristics of the model as the coefficient of determination characterizing the share of variation of the studied trait under the influence of external and internal factors, Fisher's coefficient, which evaluates the statistical significance of the resulting model. Based on the results of comparing the characteristics of adequacy and accuracy, the final choice of the predictive model is made.

● Building on a formalized model of forecasts and using the results of modeling in system management involves obtaining point forecasts that characterize the prospects for the development of the research system. In addition to these, interval forecasts can be constructed that carry a higher probability of obtaining intervals in which the characteristics of the system may fluctuate. It should be noted that forecasting is of a probabilistic nature and will be reliable only if the same patterns of development operate during the lead time that took place at the stage of system research.

The use of forecasting results in making managerial decisions is a creative process and requires not only theoretical knowledge in certain area, but also practical experience on working with the research system. At the moment, scientific research has advanced far in the development of information and analytical technologies for predicting the activities of organizations. For example, technologies of neural network forecasting, fuzzy logic, a number of specialized multifunctional analysis and forecasting programs, such as Statistica, SPSS, Stadia, VSTAT, Project Exspert and a number of other software products are known. For operational monitoring and forecasting of the results of the system functioning, as well as for educational purposes, the MS Excel package can also be used, which implements trend and regression analysis, and also allows calculating a number of additional system characteristics on the basis of a spreadsheet processor.

According to the results of the study of the management system (object) using information and analytical forecasting technologies, recommendations can be formulated for improving the activities of the organization (system), for example, focusing on achieving certain values ​​of key performance indicators that implement the organization’s development strategy, optimization cash flows, development of new perspective directions of activity . The use of modern information and analytical technologies for modeling and forecasting will help to increase the efficiency of activities in the light of the implementation of the strategy and tactics of the organization's development.

Bibliographic link

• tutorial

I have been doing time series forecasting for over 5 years. Last year I defended my dissertation on the topic " Time Series Forecasting Model from Maximum Similarity Sample”, however, after the defense, there were quite a few questions left. Here is one of them - general classification of forecasting methods and models.

Usually, in the works of both domestic and English-speaking authors, they do not ask themselves the question of the classification of forecasting methods and models, but simply list them. But it seems to me that today this area has grown and expanded so much that, even if the most general, classification is necessary. Below is my own version of the general classification.

What is the difference between a forecasting method and a model?

Prediction Method represents a sequence of actions that need to be performed to obtain a forecasting model. By analogy with cooking, a method is a sequence of actions according to which a dish is prepared - that is, a forecast is made.

Prediction Model is a functional representation that adequately describes the process under study and is the basis for obtaining its future values. In the same culinary analogy, the model has a list of ingredients and their ratio, which is necessary for our dish - a forecast.

The combination of method and model form a complete recipe!

It is now customary to use English abbreviations for the names of both models and methods. For example, there is the famous autoregression integrated moving average extended (ARIMAX) forecasting model. This model and its corresponding method are usually called ARIMAX, and sometimes the Box-Jenkins model (method) after the authors.

First we classify the methods

If you look closely, it quickly becomes clear that the concept of " forecasting method"much broader concept" predictive model". In this regard, at the first stage of classification, methods are usually divided into two groups: intuitive and formalized.

If we recall our culinary analogy, then even there we can divide all recipes into formalized ones, that is, written down by the number of ingredients and the method of preparation, and intuitive, that is, nowhere recorded and obtained from the experience of the culinary specialist. When do we not use a prescription? When the dish is very simple: fry potatoes or boil dumplings, you don’t need a recipe. When else do we not use the recipe? When we want to invent something new!

Intuitive forecasting methods deal with the judgments and assessments of experts. To date, they are often used in marketing, economics, politics, since the system, the behavior of which must be predicted, is either very complex and cannot be described mathematically, or very simple and does not need such a description. Details on such methods can be found in .

Formalized Methods- forecasting methods described in the literature, as a result of which forecasting models are built, that is, they determine such a mathematical dependence that allows you to calculate the future value of the process, that is, make a forecast.

On this, the general classification of forecasting methods, in my opinion, can be completed.

Next, we make a general classification of models

Here it is necessary to proceed to the classification of forecasting models. At the first stage, the models should be divided into two groups: domain models and time series models.

Domain Models- such mathematical forecasting models, for the construction of which the laws of the subject area are used. For example, a model used to make a weather forecast contains the equations of fluid dynamics and thermodynamics. The forecast of population development is made on a model built on a differential equation. The prediction of the blood sugar level of a person with diabetes is made on the basis of a system of differential equations. In short, such models use dependencies that are specific to a particular subject area. Such models are characterized by an individual approach to development.

Time series models- mathematical forecasting models that seek to find the dependence of the future value on the past within the process itself and calculate the forecast on this dependence. These models are universal for various subject areas, that is, their general form does not change depending on the nature of the time series. We can use neural networks to predict air temperature, and then apply a similar model on neural networks to predict stock indices. These are generalized models, like boiling water, into which if you throw a product, it will boil, regardless of its nature.

Classifying time series models

It seems to me that to compose general classification domain models is not possible: how many areas, so many models! However, time series models lend themselves easily to simple division. Time series models can be divided into two groups: statistical and structural.

AT statistical models the dependence of the future value on the past is given in the form of some equation. These include:

1. regression models (linear regression, non-linear regression);
2. autoregressive models (ARIMAX, GARCH, ARDLM);
3. exponential smoothing model;
4. model based on the maximum similarity sample;
5. etc.

AT structural models the dependence of the future value on the past is given in the form of a certain structure and rules for moving along it. These include:

1. neural network models;
2. models based on Markov chains;
3. models based on classification-regression trees;
4. etc.

For both groups, I have indicated the main, that is, the most common and detailed forecasting models. However, today there are already a huge number of time series forecasting models, and for making forecasts, for example, SVM (support vector machine) models, GA (genetic algorithm) models, and many others have begun to be used.

General classification

Thus we got the following classification of models and forecasting methods.

1. Tikhonov E.E. Forecasting in market conditions. Nevinnomyssk, 2006. 221 p.
2. Armstrong J.S. Forecasting for Marketing // Quantitative Methods in Marketing. London: International Thompson Business Press, 1999, pp. 92–119.
3. Jingfei Yang M. Sc. Power System Short-term Load Forecasting: Thesis for Ph.d degree. Germany, Darmstadt, Elektrotechnik und Informationstechnik der Technischen Universitat, 2006. 139 p.

UPD. 11/15/2016.
Gentlemen, it has reached insanity! Recently, I was sent an article for the VAK edition with a link to this entry for review. I draw your attention to the fact that neither in diplomas, nor in articles, and even more so in dissertations can't link to the blog! If you want a link use this one: Chuchueva I.A. MODEL OF PREDICTION OF TIME SERIES ON THE SELECTION OF THE MAXIMUM SIMILARITY, dissertation… cand. those. Sciences / Moscow State Technical University. N.E. Bauman. Moscow, 2012.

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Before the advent of modern IT, there were no wide opportunities to use effective economic and mathematical models directly in the process of economic activity. In addition, the use of existing forecasting models for analytical purposes did not put forward such high requirements for their information support.

Fundamentals of forecasting technologies

When building a predictive system from scratch, it is necessary to resolve a number of organizational and methodological issues. The first ones include:

• - training of users in methods of analysis and interpretation of forecast results;
• - determination of directions for the movement of predictive information within the enterprise, at the level of its divisions and individual employees, as well as the structure of communications with business partners and authorities;
• - determination of the timing and frequency of forecasting procedures;
• - development of principles for linking the forecast with long-term planning and the procedure for selecting options for the results obtained when drawing up an enterprise development plan.

The methodological problems of building a forecasting subsystem are:

• - development of the internal structure and mechanism of its functioning;
• - organization of information support;
• - development of software.

The first problem is the most difficult, since to solve it it is necessary to build a set of forecasting models, the scope of which is a system of interrelated indicators. The problem of systematization and evaluation of forecasting methods is one of the central ones here, since in order to select a specific method, it is necessary to conduct their comparative analysis. A variant of the classification of forecasting methods, taking into account the peculiarities of the knowledge system that underlies each group, can be summarized as follows: methods of expert assessments; methods of logical modeling; mathematical methods.

Each group is suitable for solving a certain range of tasks. Therefore, practice puts forward the following requirements for the methods used: they must be focused on a specific forecasting object, must be based on a quantitative measure of adequacy, and be differentiated in terms of the accuracy of estimates and the forecasting horizon.

The main tasks that arise in the process of creating a predictive system are divided into:

• - building a system of predictable processes and indicators;
• - development of an apparatus for economic and mathematical analysis of predicted processes and indicators;
• - concretization of the method of expert assessments, selection of indicators for examination and obtaining expert assessments of some predicted processes and indicators;
• - forecasting indicators and processes with indication of confidence intervals and accuracy;
• - development of methods for interpretation and analysis of the obtained results.

The work on the information and mathematical support of the forecasting system deserves special attention. The process of creating software can be represented as the following steps:

• - development of a methodology for structural identification of the object of forecasting;
• - development of methods for parametric identification of the forecasting object;
• - development of methods for predicting trends;
• - development of methods for predicting the harmonic components of processes;
• - development of methods for assessing the characteristics of random components of processes;
• - creation of complex models for predicting indicators that form an interconnected system.

The creation of a forecasting system requires an integrated approach to solving the problem of its information support, which is usually understood as a set of initial data used to obtain forecasts, as well as methods, methods and tools that ensure the collection, accumulation, storage, search and transmission of data in the process of functioning of the forecasting system. and its interaction with other enterprise management systems.

Information support of the system usually includes:

• - information fund (database);
• - sources of formation of the information fund, flows and methods of data receipt;
• - methods of accumulation, storage, updating and retrieval of data that form the information fund;
• - methods, principles and rules of data circulation in the system;
• - methods for ensuring the reliability of data at all stages of their collection and processing;
• - methods of information analysis and synthesis;
• - ways of unambiguous formalized description of economic data.

Thus, the following main components are required to implement the forecasting process:

• - sources of internal information, which is based on management and accounting systems;
• - sources of external information;
• - specialized software that implements forecasting algorithms and analysis of results.

Given the importance of solving the problem of forecasting for market participants, it is advisable to check the quality of the proposed methods and algorithms, as well as technologies in general, using specially selected (test) initial data. A similar verification method has been used for a long time in assessing the adequacy of mathematical tools designed for nonlinear optimization, for example, using the Rosenbrock and Powell functions.

Confirmation (or verification) of the quality and performance of the forecasting technology is usually carried out by comparing a priori known model data with their predicted values ​​and evaluating the statistical characteristics of forecast accuracy. Let's consider this trick in a situation where the process models are an additive set of the trend Tt, seasonal (harmonic) and random components.

At present, a wide variety of software tools have become widespread, providing, to one degree or another, the collection and analytical processing of information. Some of them, such as MS Excel, are equipped with built-in statistical functions and programming tools. Others, especially inexpensive accounting and management accounting programs, do not have such capabilities or analytical capabilities are not implemented in them sufficiently, and sometimes incorrectly. However, this is, unfortunately, inherent in some more powerful and multifunctional enterprise management systems. This situation is apparently explained by a shallow analysis on the part of the developers of the properties of the forecasting algorithms they have chosen and their uncritical application. For example, judging by the available sources, zero-order exponential smoothing is often used as the basis for predictive algorithms. However, this approach is valid only in the absence of a trend in the process under study. In fact, economic processes are non-stationary, and forecasting involves the use of more complex models than models with a constant trend.

It is interesting to trace the path of development of domestic automated banking systems from the perspective of the topic under consideration. The first banking systems were based on rigid technology, constantly requiring changes or additional software. This prompted developers of financial software, following the principles of openness, scalability and flexibility, to use industrial DBMS. However, by themselves, these DBMS turned out to be unsuitable for solving high-level analytical problems, which include the problem of forecasting. To do this, it was necessary to use additional technologies for data storage and operational analytical processing, which ensured the operation of decision support systems for financial and credit institutions and for making forecasts. The same approach is used in complex enterprise management systems.

Another direction of modern applied use of forecasting methods based on IT is the solution of a wide range of marketing tasks. An illustration is the SAS Churn Management Solution for Telecommunications software. It is intended for telecommunications operators and allows, as its developers claim, to build predictive models and use them to assess the likelihood of an outflow of certain categories of customers. The basis of this software is the Scalable Performance Data Server distributed database server, tools for building and administering data warehouses and data marts, Enterprise Miner data mining tools, SAS / MDDB Server decision support system, as well as auxiliary tools.

To ensure the competitiveness of newfangled CRM-systems in the list of their advanced features, as well as for automated banking systems, reporting functions are included that use OLAP technologies and allow, to a certain extent, to predict the results of marketing, sales and customer service.

There are quite a lot of specialized software products that provide statistical processing of numerical data, including individual elements of forecasting. These products include SPSS, Statistica, etc. These tools have both advantages and disadvantages, which significantly limit the scope of their practical application. It should be noted here that the assessment of the suitability of specialized mathematical and statistical software tools for solving forecasting problems by ordinary users who do not have special training requires a separate serious study and discussion.

However, solving forecasting problems for consumers from small and medium-sized businesses with the help of powerful and expensive information systems and technologies is practically impossible, primarily for financial reasons. Therefore, a very promising direction is the development of the analytical capabilities of existing and widespread low-cost accounting and management accounting systems. Developed additional reports based on specific business processes and containing the necessary analytical information for a particular user have a high ratio of "efficiency - cost".

Some software developers create entire lines of analytical tools. For example, Parus Corporation offers Parus-Analytics and Triumph-Analytics solutions for a wide range of users from small and medium-sized businesses. More complex tasks of analytical processing of forecast information are integrated into the Parus system in the form of a so-called situational center. According to Dmitry Sudarev, manager for the development of circulation solutions, it was decided to develop and implement software products that allow moving from simple accounting of facts in the enterprise's activities to information analysis. At the same time, a transition was planned from automating the work of accountants and middle managers to processing information for top management. Taking into account the possible circle of consumers, Parus-Analytics and Triumph-Analytics do not impose special requirements on the software and hardware environment, however, the Triumph-Analytics solution is implemented on the basis of MS SQL Server, which provides it with greater opportunities for predicting the processes under study , in particular, the harmonic component of forecasts is taken into account.

The value of the forecast increases many times when it is directly used in the management of the enterprise. Therefore, an important direction is the integration of forecasting systems with systems such as Kasatka, MS Project Expert, etc. strategic planning. Such a purpose predetermines the need to identify long-term trends and take them into account in planning. The forecasting horizon is determined based on the relevant goals of the organization.

The tasks of long-term development facing the Russian economy require a radical increase in management efficiency at various levels. This task is fully domestic companies. The need to solve it actualizes the development of tools for forecasting development prospects and assessing the impact of the developed strategies on the stability of the financial position of companies.

The report substantiates the need to move from purely analytical methods of describing a company to a probabilistic description through simulation of cash flows. This provides the implementation systems approach to financial forecasting and risk assessment of the company's development, which makes it currently a priority approach to building financial models in leading foreign companies.

The use of probabilistic models for predicting the development of a company taking into account risks, as the author's experience has shown, is associated with the formulation of a number of complex problems, both of a general theoretical and methodological nature, which are practically not covered in domestic and foreign specialized literature. Without their solution, it is impossible to widely introduce modern methods of financial management in Russian companies. strategic management. Among such problems, for example, is the problem of forming the entire space of variants in the model without the need for their complete enumeration, which, without compromising the accuracy of forecasting based on convergence analysis, makes it possible to reduce the number of analyzed combinations of model parameters by several orders of magnitude.

■ a standard multi-trend financial model was developed that makes it possible to predict the dynamics of cash flows and evaluate their fluctuations, including the probability of their deviations from the minimum allowable values. An example of a calculation is given that illustrates the proposed mechanism for assessing the risks of a company's insolvency;

■ Algorithms for processing initial time series are proposed, which ensure the use of empirical probability distributions along with standard ones without the need for their analytical description, which greatly simplifies the implementation of the simulation method in companies;

■ an approach to the structuring of the financial model based on its consistent “top-down” detailing is proposed, with a different degree of detailing possible depending on the goals of the analysis and the availability of initial information;

■ standard tools for automating the analysis of accounting data (obtained from the 1C system) were developed; statistical analysis of time series; plotting graphs and histograms, including for intervals of various lengths (week, month, quarter). Taken together, this makes it possible for company managers to prepare initial data for a forecasting model;

■ analyzed the features of risk assessment and proposed tools for managing the development of the company at three levels (investment project, portfolio of projects, the company as a whole), taking into account the continuity of the collection, processing and analysis of data coming both from outside and generated within the company;

■ the mechanism of sensitivity analysis was considered taking into account non-linearity; as well as an approach to assessing the total risk of a project portfolio, based, in particular, on the results of simulation modeling of individual investment projects;

The report shows the possibility of applying the proposed approach to building forecasting models to assess development prospects and the risk of insolvency not only by the company's management, but also by external structures, including higher organizations (for example, within holdings, state corporations), banks, investment and insurance companies .

Trends in forecasting the development of companies taking into account risks

AT modern conditions to succeed in the competitive struggle, companies must constantly and continuously develop. This requires not only regular product updates, improvement of technological and business processes, but also the development of special tools for financial forecasting of the consequences of actions taken for the development of the company, long-term changes in its value. Financial forecasting models based on cash flow models act as modern tools.

At the same time, in practice, companies face a number of significant problems that make it difficult to carry out forecasting on a regular basis. They are caused both by the insufficient development of a holistic risk-based financial forecasting methodology that meets the needs modern business, and the lack of organizational mechanisms and software tools for the accumulation and analysis of management information when making strategic financial decisions.

The trends of economic development observed in recent decades and the information revolution that have taken place have a significant impact on the forecasting processes in companies. These trends have changed the environment in which companies operate and have transformed the requirements for designing business forecasting models.

1.1. General economic trends

An important feature of the current stage of economic development is the complication of the external environment and the acceleration of market changes, as well as the increasing influence of world economic processes. As a result, companies today face significant large quantity market opportunities and threats. Accordingly, there has been an increase in the number of factors that can have a significant impact on the profitability and financial stability of companies' development, which requires these factors to be taken into account in forecasting models. Under these conditions, the ability to provide probabilistic forecasts and risk assessments at the output becomes not just an additional characteristic of the forecasting model, but its integral and mandatory component.

As R. Stulz points out, companies today face the task of taking into account even those threats, the probability of which is assessed as insignificant. Among a special, but increasingly significant type of such threats are the economic consequences for companies of global strategic risks associated with the depletion of natural resources, climate change, the occurrence of man-made disasters, as well as socio-political factors. Despite the objective complexity of assessing these risks, due to the growing scale of damage from them, the need for companies to develop risk modeling mechanisms as an attribute of forecasting models also increases.

Finally, increasing volatility in market conditions makes it necessary to increase the flexibility and adaptability of forecasting models. The technology for building forecasting models should provide for the possibility of quickly including new parameters in the model (lines of activity, individual items of income and expenses, etc.). This requires the simultaneous improvement of the procedures for building models and management mechanisms for their use in companies, the transition to a continuous analysis of ongoing changes in both the external and internal environment of the company.

1.2. Information Technology Development Trends

The principal feature modern stage technological development is the ever-increasing volume of information entering the company.

Computerization has provided rapid access to vast amounts of information, which was unthinkable when this data was stored on paper media, and caused a surge in the increasingly active use of databases for various purposes for the economic description of economic activity.

These changes required the adaptation of methods and processes for building forecasting models and analyzing the risks of company development.

One of the directions of such adaptation was a significant complication of analytical models, which stimulated the rapid mathematization of economic science, which is considered by many scientists as a negative factor in its development. The formation of this direction was quite natural and logical, since even before the middle of the last century, in fact, the only way to calculate the main economic indicators and describe the relationships between them in forecasting models was to use analytical dependencies. A model that did not give explicit analytical formulas was considered useless. A characteristic feature of such models was their simplification, which manifests itself, in particular, in the hypothesis of the completeness of information, determinism economic conditions as one of the basic assumptions of the neoclassical direction of economic theory.

The limitations of the analytical description of economic processes are manifested mainly in the impossibility of setting, with the help of only mathematical means, actually observed economic dependencies, the vast majority of which are probabilistic and non-linear in economics.

Increasing the power of computers made it possible to reduce the need for the use of exclusively analytical tools for assessing the profitability of management decisions. As D. Colander notes, if earlier companies were considered as relatively simple systems, the description of which could be reduced to a system of equations with analytical solutions, then the current trend is to consider companies as complex systems, which makes their full analytical description impossible. Accordingly, simulation modeling is currently becoming the main method for describing such systems. The ability to build in a spreadsheet environment provides high versatility and flexibility in setting economic dependencies, which opens up significant opportunities for companies in financial design and modeling of economic processes.

The considered trends largely determined the development of a systematic approach in management, which implies, in particular, the constant accumulation and processing of information with its subsequent transformation into an organizational knowledge base.

The fundamental importance that information acquires in the value chain in modern companies is also fully manifested in the construction of financial forecasting models. The mandatory information required to build accurate forecasts includes the statistical characteristics of the company's main economic parameters (sales volume, key expense items, etc.). Therefore, statistical analysis is an organic element in creating a forecasting model.

Thus, in the financial forecasting model, all the information available for formalization in the form of cash flows, which is necessary for making strategic decisions, is accumulated. That is, the use of a forecasting model provides an increase in the systematic management of the company. And these models themselves can naturally be considered as an element of structural capital - a subsystem of the company's intellectual capital.

The use of simulation modeling makes it possible to ensure the implementation of another basic principle of a systematic approach - consideration of the entire space of possible, according to experts, options, which opens the way for a probabilistic description of the resulting cash flows of the model.

At the same time, we emphasize that the term “complete space of variants” should be understood in a statistical sense. We are not talking about a mechanical enumeration of all theoretically possible combinations of the values ​​of the studied parameters of the model, which in most cases is technically impossible. In the modeling process, only statistically significant variants (having a probability of occurrence greater than, for example, 0.01%) should be taken into account, determining their optimal number based on convergence analysis algorithms.

Building a complete space of options when modeling risks allows for each calculation step of the model (for example, a quarter) to determine the probabilistic characteristics of the company's cash flows: the mathematical expectation of the cash flow, its minimum and maximum values ​​(Fig. 1.1).

Such an analysis makes it possible to identify periods in which the resulting cash flow of the company is stable, as well as periods of its decline and rise. In addition, the company has a real chance to calculate the amount of risk, which in this case is defined as the integral probability that the value of the resulting cash flow will go out of the acceptable range (for example, become negative).

Rice. 1.1. Risk modeling allows you to present the company's cash flow as a corridor of its possible change

Maintaining the company's cash flow within acceptable limits contributes to the growth of its financial stability. In addition, risk modeling allows you to analyze and select the most effective development strategies, enhancing management flexibility and increasing the overall competitiveness of the company.

Thus, conducting a probabilistic analysis of the company's cash flows significantly expands the amount of information that can be taken into account in the process of making strategic decisions. The obtained quantitative risk assessments, in our opinion, should be considered as a fundamental characteristic of the company's development and one of the most important indicators to be taken into account when making decisions at various levels of management.

The complexity of economic systems dictates the need to take into account such a property as the multi-level systems when building models for their forecasting. With regard to the task of building models for the development of companies, three levels can be distinguished: a separate investment project, a portfolio of projects, and the company as a whole. Although the problems and methods of financial modeling at each of these levels are widely reflected in the scientific literature, one should recognize the insufficient theoretical development of this issue. Features of development risk assessment at the three indicated levels are analyzed in the third section of the report.

An analysis of the considered problems shows that the task of developing a development forecasting model should not be reduced only to the construction of financial models and their quantitative, including probabilistic analysis. The central role of the forecasting model in the system of strategic management of a company seems to be fundamental, in which it acts not just as a formal financial plan, but as the main tool for assessing the profitability of the developed development strategies, as well as as a result of the accumulation and processing of huge amounts of information stored in the company.

Therefore, it can be argued that for the effective application of the forecasting model, it is necessary to transform the company's management system so that it allows the accumulation of information required for the development of forecasts and risk assessment. It seems that the ability to assess the risks of decisions made on the basis of available statistical and expert information can be considered as one of the core competencies management of any modern company.

This makes it necessary to develop management technology forecasting the development of the company, which is a subsystem for managing its strategic development. An important element of such a technology should be the construction of a personnel training system, although it requires significant investments in improving its qualifications, but in many respects it determines the innovative potential of the company, and hence its competitiveness.

1.3. General technology for building a model for predicting the development of a company, taking into account risks

The key role played by the quality of the initial data for the accuracy of the company's future development forecasts dictates the general logic of building an internal forecasting model (Fig. 1.2). Based on a comprehensive study of business processes and statistical analysis of the main items of income and expenses of the company, managers determine the structure of the model, set the initial data and dependencies between the main factors. A preliminary model is then built from the historical data in order to verify that the forecast obtained with the help of it corresponds to the actual cash flows of the company. After debugging the model, it is corrected taking into account expert estimates and used to build a forecast for a certain number of periods within the planning horizon. In the future, periodic monitoring of the development of the company is carried out in order to take into account changes in the external and internal environment of the company.

Rice. 1.2. The general scheme of the process of building a model for predicting the development of a company, taking into account risks

Problems of preparing initial data for a forecasting model

As is known, the quality of the information used in it plays a decisive role in the accuracy of forecasts obtained using any model. Therefore, the preparation of initial data for the model is the most important task, which requires the company to have both special analytical tools and management procedures.

Preparation of initial data for the model is impossible without the active use of statistical analysis, designed to identify patterns and trends in the main items of income and expenses of the company.

In the process of statistical analysis, a number of complex problems arise, such as working with non-typical probability distributions, identifying trends, ensuring data homogeneity, and others that are not sufficiently or not considered at all in the special literature.

We also note that statistical analysis should not be considered only as a set of formalized procedures for processing data series. As emphasized by E.F. Siegel, “statistics is the art and science of collecting and analyzing data. Statistical methods should be considered as an important part of the decision-making process, allowing the development of informed strategic decisions that combine the intuition of a specialist with a thorough analysis of the available information. The use of statistics is becoming an increasingly significant competitive advantage. Thus, statistical analysis of data is a means of gaining a deeper understanding of the economics of a company − mandatory condition building an accurate model for its prediction.

2.1. Input data types

In the process of analyzing the initial data, it is necessary to take into account their differences in terms of the degree of uncertainty and the nature of changes over periods. Based on this, three types of parameters can be distinguished:

1. Parameters whose values ​​are constant in all periods during the planning horizon (for example, tax rates, rentable area);

2. Parameters, the values ​​of which remain constant within each individual period (calculation step), but may change from period to period (for example, electricity prices);

3. Parameters whose values ​​change randomly within a certain period (for example, sales volume). At the same time, their mathematical expectations over the periods can remain constant or change in accordance with a certain trend.

From the above classification, it is clear that the most difficult parameters for analysis and forecasting are the parameters of the third type, which change randomly. For their correct modeling in the course of analyzing the initial data, it is necessary to determine not only the expected values ​​and trends, but also the ranges of their values, as well as the probability distribution law. Therefore, further attention will be paid to the parameters of the third type.

As can be seen from Table 2.1, the main source of initial information for the statistical analysis of parameters of the third type is accounting and management accounting data. Obtaining this data usually does not cause fundamental difficulties, since their collection and storage in companies is mandatory, given the importance of these parameters.

Table 2.1. Examples of common input data parameters, usually random in nature

2.2. Challenges in Ensuring Relevance and Homogeneity of Source Data

Statistical analysis of the initial series of each analyzed parameter is designed to identify its most significant characteristics, which are then used in modeling predictive values.

At the same time, in order to ensure that the forecasting model takes into account all available information, it seems reasonable to use the entire available time series of this parameter in the most detailed form in the statistical analysis of each studied parameter of the model (for example, daily values ​​of product sales for three years).

Since cash flows for various items of income and expenses occur at different intervals (daily, weekly, monthly, etc.), the problem arises of aggregating the values ​​of all studied parameters by intervals in order to correspond to the calculation step chosen in the model.

To do this, the original series is divided into intervals corresponding to the required calculation step. For example, when aggregating cash inflows to the company's current account by quarters, all inflows received for the period from 01.04 to 30.06 of the current year will be assigned to the second quarter. Then all values ​​of the studied parameter within each interval are replaced (approximated) by mathematical expectations (Fig. 2.1).

Rice. 2.1. Graphical representation of the approximation of series values ​​by their mathematical expectations over intervals

Rice. 2.2. An example of schedules for the receipt of funds to the company's current account, aggregated by intervals(a - by weeks; b - by months; in - quarterly). Source: author's calculations

As can be seen from the graphs, with an increase in the size of the interval, the fluctuations are smoothed out, which facilitates the subsequent modeling of the parameter under study.

The quarterly chart also most accurately shows the presence of a seasonal component, which should be taken into account when modeling trends.

In addition, the comparison of these graphs demonstrates the value of analyzing the most detailed information. On fig. Figures 2.2a and 2.2b draw attention to the increase in the volatility of the parameter, which is invisible on the chart of quarterly values ​​(Fig. 2.2c). The reason for this increase was the increase in the share of large orders in the company's sales structure, which increased the unevenness of cash inflows.

The increase in volatility is even more noticeable in the company's receivables chart (Figure 2.3).

Thus, the considered example testifies to the value of series analysis at each of the levels of data aggregation, which provides additional significant information about the studied parameter of the model.

Rice. 2.2a and 2.2b illustrate another fundamental problem that arises in the process of statistical analysis of initial data - the problem of their heterogeneity. The appearance of additional factors affecting the parameter under study, or a change in the ratio between the factors often lead to a change in the probabilistic characteristics of the series (in this case, an increase in the variance).

The ultimate goal of preparing initial data is to use in the model the maximum amount of information that is most relevant at the time of decision making. Significant changes in technology, the market situation or the legal framework may lead to the fact that some of the available data for previous periods are no longer relevant, and their inclusion in the construction of the model can reduce the accuracy of the forecast.

Rice. 2.3. Accounts receivable schedule (by days)

Rice. 2.4. Histogram of Probability Densities of Sales Volume(a - general, b - product 1, in - product 2)

Ensuring homogeneity becomes one of the key criteria in the decomposition of the studied parameters, determining the optimal degree of detail of the model. As an example, consider a histogram of a company's sales (Figure 2.4a).

The pronounced bimodality of the overall distribution, caused by the presence of two dominant factors, is largely eliminated when divided into two products (Fig. 2.4b, 2.4c). This indicates the need to break down the company's sales by product in order to obtain more accurate distributions.

2.3. The Problem of Identification of Probability Distribution Laws

One of the most difficult problems in simulation modeling is the identification of the type of probability distribution of random variables. Insufficient attention paid to this problem in the specialized literature, apparently, can be explained by a common misconception that the distributions of economic indicators correspond to or can be reduced to typical distribution laws (especially to the normal law). This assumption allows using well-developed mathematical tools for data analysis.

However, working only with typical distributions in many cases leads to ignoring deviations in the form of actually observed distributions, which manifest themselves, in particular, in asymmetries and outliers. Moreover, as the results of the analysis carried out by the author have shown, the distributions of most financial indicators reflecting the economy of a real sector company differ significantly from the typical ones.

The distributions studied in the course of this scientific study can be divided into four groups.

First group. Distributions similar to exponential:

The cost of one order;

Cost of materials (by days);

Inflow and outflow of funds on the current account (by days);

Turnover of funds on the current account (by days).

Second group. Distributions similar to the Poisson distribution:

The cost of concluded orders (weekly);

Current account balance (by days).

Third group. Distributions close to symmetric (including normal):

Change in cash (taking into account the company's reserves (by days);

Accounts payable (by days);

Differences between total accounts payable and accounts receivable.

Fourth group. Bimodal and other obviously non-standard distributions.

Total revenue (by days);

Cash balance (taking into account the company's reserves (by days);

Accounts receivable (by days).

A number of authors note that the distributions of many economic quantities do not correspond to the normal law. As pointed out, for example, by A.I. Orlov, “in econometrics, the distribution of the results of economic and technical and economic observations almost always differs from normal” .

Attempts to ignore the deviations identified during the analysis can result in a distortion of estimates of the expected variability of the parameters of the forecasting model. As a result, there is a loss of significant information about the probability distribution and, ultimately, a decrease in the accuracy of forecasts.

A very common method for converting non-standard distributions into typical ones is the logarithm of the original series of values, which usually eliminates a serious distribution skewness. However, as modeling experience has shown, the logarithm has serious limitations. They are due to the fact that during the reverse transformation of the mathematical expectation and standard deviation (from logarithmic to initial), the parameters of the series obtained by calculation differ from their actual values. This significantly complicates the application of this method in practice.

Rice. 2.9. Comparison of the empirical and normal distribution of the company's accounts payable (- - empirical distribution; -- - normal distribution).

In our opinion, a more universal solution to this methodological problem is the use of the so-called empirical distribution obtained directly from the analysis of a series of data without its analytical description (provided that it is stable).

To illustrate the possible distortions of the distribution of the parameter when it is artificially reduced to the standard one in Fig. Figure 2.9 compares the actual empirical distribution of the company's accounts payable (solid line) and the generated normal distribution (dashed line), which have the same values ​​of mathematical expectation and standard deviation (calculated during the analysis of the original series). The discrepancy between the graphs indicates the incorrectness of using the normal distribution instead of the actually observed one.

To overcome the difficulties that arise when working with empirical distributions compared to typical ones, it is necessary to have appropriate tools for generating random numbers, transforming these distributions taking into account the trends of mathematical expectations and standard deviations, and detailed statistical analysis of the initial values ​​of time series.

2.4. Generation of empirical distributions

Most universal method generation of an empirical distribution is rightly considered the method of linear approximation. According to this method, the generation of random numbers is carried out in several stages:

1. The original series is divided into h intervals (pockets) of variable or constant length. Variable length bins result in "long" bins in distribution regions with few values ​​and "short" bins in distribution regions with a large number of values. This makes it possible to take into account the complex form of distributions more correctly, thereby increasing the generation accuracy.

2. For each interval, the hit frequencies of the values ​​of the original series and the corresponding integral probability are calculated (see Table 2.3).

3. The required number of random numbers is generated using a standard uniform distribution generator.

4. Each of the numbers generated according to the uniform law is transformed using data similar to those given in Table 2.2 to obtain random variables with the desired empirical distribution.

Table 2.2. An example of an empirical distribution frequency table for intervals of constant length

2.5. Ways to Specify Trends for an Empirical Distribution

The proposed approach to modeling trends in empirical distributions differs from the mechanism for setting trends for typical distributions.

Recall that for typical distributions, a trend is first set for distribution parameters, such as mathematical expectation, standard deviation, and others. Based on the values ​​of the distribution parameters calculated for each period, random numbers are generated using the analytical formulas of the corresponding distribution. In this case, a trend is automatically provided for all points of a typical distribution by periods.

Since there is no analytical description for empirical distributions, the trend must be set immediately for all distribution points. As will be shown below, this provides the required trend of the mathematical expectation and variance (standard deviation).

In accordance with the method of linear approximation, when modeling, it is sufficient to work not with individual values, but with the boundaries of the intervals (similar to those given in column 1 of Table 2.2) and the frequencies of the values ​​falling into the formed pockets.

The proposed approach provides two ways to set a trend for an arbitrary distribution.

1. Only the mathematical expectation of the series changes from period to period

The transformation of the original series, taking into account the trend, is carried out by adding the same number A to each value of this series. Then the mathematical expectation of the period t + 1 is calculated as follows:

where M(X) t , M(X) t+1 are the mathematical expectations of the parameter under study in periods t and t+1; x t — i-th value parameter in period t; n is the total number of generated random values ​​(the same for all periods).

It is easy to establish that, taking into account (1), for this case, the dispersion of the parameter t + 1 will remain unchanged:

where D t , D t+1 are dispersions of the studied parameter in periods t and t+1;

Graphically, in the presence of a positive trend, the histogram of parameter values ​​for period t+1 shifts along the X axis to the right by A.

2. From period to period, both the mathematical expectation and the standard deviation change

In this case, the transformation of the original series, taking into account the positive trend, is carried out by multiplying each value of this series by the same number k. Then the mathematical expectation of the period t+1 is calculated by the formula:

The dispersion of the parameter t+1 is calculated by the formula:

Accordingly, the standard deviation a, taking into account the trend in period t + 1, is calculated by multiplying its value in period t by k.

The coefficient of variation in this method remains unchanged.

2.6. Tools for automating the collection and statistical analysis of initial data

Due to the complexity of the procedures for processing the initial time series, in practice they should be carried out automatically, using standard software.

Table 2.3. An example of an account table in 1C

Table 2.4. View of the converted table for processing by means of Excel

When obtaining initial series from various computer databases, the problem of unifying the form of providing information for its subsequent analysis arises. For example, to process data on accounts obtained from the widespread accounting system 1C (Table 2.3), they are converted into a table of the form Table. 2.4, which serves as the basis for the formation of the initial time series.

Features of development risk assessment at three levels of management in the company

As noted above, forecasting the development of a company, taking into account risks, should be carried out at three levels: the level of an individual investment project, a portfolio of projects, and the company as a whole. This is due to the difference in tasks at each of the levels (Table 3.1), which determine the features of the developed models and analysis algorithms.

Table 3.1. The difference between the tasks to be solved at three levels of investment management in the company

3.1. Individual investment project level

Significant knowledge intensity, the time span of the transformation of invested resources into an increase in the value of the company, as well as the high uncertainty of potential results, indicate the main form of investment in the company - the form of an investment project. Investment projects act as sources of formation of future competitive advantage. Therefore, in the process of developing each investment project, it is extremely important to receive the most complete information about the prospects of the project in time, not only in terms of the amount of net cash flow that this project is able to generate, but also from the position of determining the range of possible cash flow fluctuations. Quantitative project risk analysis methods play a key role in providing company management with this information.

The basis for quantitative risk assessment of an investment project is the model of its cash flows. The first stage of its development is to determine the structure of income and expenses of the project, forecast their values, taking into account the dynamics of changes during the planning horizon.

The cash flow model of an investment project serves as the basis for calculating its performance indicators: net present value (NPV), discounted payback period (DPP), profitability index (PI) and others. The resulting values ​​of these indicators reflect the predicted profitability of the project for the company in conditions when all parameters take their most probable (basic) values.

At the next stage, when conducting a sensitivity analysis of the project, the model parameters that have the strongest impact on the economic efficiency of the investment project are determined. In its classical form, sensitivity analysis is reduced to the calculation of dimensionless sensitivity coefficients that reflect the elasticity of project performance indicators.

However, in practice, when conducting sensitivity analysis, it must be remembered that the traditional approach is based on the assumption that the sensitivity functions are linear. In reality, the sensitivity functions for many parameters of the project cash flow model are non-linear. For example, as shown by the results of the analysis of the sensitivity functions of the investment project carried out by the author (Table 3.2), of the fifteen parameters of the model, the sensitivity function NPV turned out to be non-linear for four parameters, PI for eight, and DPP for all fifteen. A well-known example of a non-linear sensitivity function, widely considered in the literature, is the function of changing the NPV of a project with a change in its discount rate . Moreover, as A.A. Kugaenko, when modeling economic systems, “linear interdependencies are practically absent” .

Table 3.2. An example of the analysis of sensitivity functions of investment project parameters for non-linearity

Conducting a sensitivity analysis plays important role in increasing the consistency of justification of the investment project. Its results make it possible to determine which model parameters require mandatory consideration of the variability of their values.

The inclusion in the cash flow model of all possible options for the values ​​of these parameters, carried out with the help of simulation, turns it from a basic one into a probabilistic one. Simulation modeling of an investment project is carried out in several stages using MS Excel spreadsheets:

1. The initial parameters of the cash flow model are selected, for which simulation modeling will be carried out. For each of them, the distribution law (uniform, normal, Poisson, etc.) and distribution parameters are determined.

2. For each parameter, m random numbers are generated using standard Excel functions. The number of generated numbers is the same for all parameters and usually ranges from 1000 to 50000.

3. Based on the generation results, m combinations of random numbers are formed for the selected parameters. One combination corresponds to one row of the Excel table.

4. For each combination of parameter values, the project performance indicators are calculated. To do this, using computer program written in Visual Basic for Applications, all combinations of input parameter values ​​are sequentially substituted into the cash flow model. The resulting performance indicator values ​​for each combination are placed in the corresponding row of the Excel spreadsheet.

5. In Excel, the rows of the table of random values ​​of the initial calculation data are sorted in ascending order of the efficiency indicator (for example, NPV).

6. Each line of the table is assigned a certain integral probability. So, if there are 1000 rows in the array, then rows i and i + 1 will correspond to integral probabilities that differ by 0.1%.

7. The integral probability of a negative NPV of the project is calculated. To do this, the number of rows in which NPV is negative is divided by the total number of rows in the table.

The considered approach to simulation modeling allows not only to calculate the expected values ​​of the investment project performance indicators, but also to obtain an additional criterion that reflects the risk of the project: the integral probability that the value of the performance indicator will be in the region of unacceptable values.

Thus, the main task of financial modeling and quantitative risk assessment at the level of an individual investment project is the most detailed study of the potential for creating market value for the company and the magnitude of possible deviations of its cash flows. However, to ensure that investment projects being developed are in line with the company's strategic goals, they need to be reviewed at the portfolio level.

3.2. Portfolio level of investment projects

Since the 1970s, when the Boston Consulting Group matrix was proposed, the portfolio approach has become widespread as a tool for planning competitive strategies and allocating capital between products (or individual lines of business) of companies. It is equally important to consider as a portfolio a set of investment projects under development, many of which, as noted above, are the basis of the company's future products that form its cash flow.

From the point of view of managing the competitiveness of a company, a portfolio of investment projects can be viewed as a portfolio of its future competitive advantages. Therefore, decisions made at the portfolio level, the most important of which are the selection of investment projects and the distribution of capital between them based on a multi-criteria approach, largely determine the areas of competitiveness growth that a company chooses for itself when developing a development strategy.

Since projects have different degrees of riskiness, it is necessary to control the overall risk level of the project in order not to exceed its maximum acceptable value for the company.

In our opinion, the most universal approach to assessing the total risk of a portfolio of projects is to use the results of simulation modeling carried out for each of the projects included in the portfolio.

The initial data for the calculation are the probability distributions of NPV for each of the r projects. The calculation procedure consists of the following steps:

1. N combinations of NPV are formed. To do this, the table of random values ​​of each project is sorted in ascending NPV, after which the column of NPV values ​​is transferred to the table, the general view of which is presented in Table. 3.3.

2. The total PV rest of the portfolio is calculated for each combination.

3. Table 3.3 is sorted in ascending order by the PV rest of the portfolio.

4. Each combination is assigned an integral probability, determined by dividing the row number of the table in which this combination is located by the total number of combinations N.

5. The integral probability of a negative PV residual of the portfolio is determined.

Note that this method assumes that the number of random NPV values ​​of all projects is the same.

In the event that simulation modeling was not used to assess the risks of some of the company's projects and their probabilistic characteristics (M(X) and a) were obtained by some other method, these projects can also be included in the calculation. To do this, NPV values ​​are generated based on the specified probabilistic characteristics and the NPV distribution law of the project.

Table 3.3. General form portfolio risk assessment tables based on the results of simulation modeling of projects included in the portfolio

Thus, managing a portfolio of investment projects taking into account risks increases the balance of the portfolio and the flexibility of making strategic decisions, which provides a significant potential for increasing the company's competitiveness. However, when developing a development strategy, it is extremely important to be able to assess its impact on the financial position and risk of the company as a whole.

3.3. Company level as a whole

At present, the task of developing a technology for quantitative assessment of investment development risks goes beyond the investment analysis of both individual projects and the portfolio. In today's dynamically changing external environment, it becomes necessary to apply a systematic approach to risk analysis and financial design of the company's strategic development as a whole. This involves the development of a financial model of the company, which makes it possible to predict the dynamics of its cash flows, taking into account the chosen development strategy, the likelihood and amount of possible damage in the event of adverse changes in the market environment, and also to develop measures to minimize this damage.

The basis for quantitative risk assessment at this level is a risk-based company development forecasting model. It allows you to calculate the total cash flows of the company and conduct their probabilistic analysis, assess the impact of the developed development strategies and expected changes in the company's competitive position. The model must be flexible, constantly developed and improved by the company's managers, taking into account the ongoing changes. Thus, the adaptability of the forecasting model is one of the key conditions that enable its effective application for quantitative risk assessment at the company level.

To implement these properties, the forecasting model, when implemented in a company, must be implemented in the form of a software package that automates the procedures for building a multi-period cash flow model, generating random numbers, simulation modeling and statistical analysis of forecasting results. This makes it possible to ensure the efficiency of obtaining results when modeling various options and development strategies.

The most important element of the initial data in the forecasting model is the description of the trends of the changing parameters.

The most universal and flexible method for specifying parameter changes is the direct entry of their values ​​by period. This, in particular, makes it possible to use time dependencies in the model (for example, planned sales volumes, product price changes, etc.) obtained as a result of marketing research. This way of setting is also necessary for parameters that change irregularly (for example, the cost of renting premises, which usually remains unchanged throughout the year). In many cases, to describe the change in parameters whose values ​​change in each period, it is much more convenient to set trends in the form of a series of values, which is an arithmetic or geometric progression.

For parameters whose values ​​change randomly, it is necessary to be able to set changes in the value of the standard deviation. There are several different ways to change it:

a) the standard deviation remains constant for all periods, regardless of the change in the mathematical expectation;

b) the standard deviation varies linearly;

c) the standard deviation changes in such a way that the coefficient of variation, equal to the ratio of the standard deviation to the mathematical expectation, remains constant.

As modeling experience has shown, taking into account changes in the standard deviation has a significant impact on the results of assessing the risk of a company's insolvency, so the availability of various ways to set the standard deviation is important to improve forecasting accuracy.

Another significant factor that should be taken into account when setting the initial data is the need to specify the limiting values ​​of the parameters, which are due to their economic nature. For example, the sales volume cannot be negative or exceed the value of the maximum market volume. Similarly, costs, which are cash outflows, cannot become positive if they are reduced in absolute value. For this reason, the probability distributions of the parameters become truncated.

In the process of simulation modeling, the program detects random values ​​that go beyond the limit values ​​and corrects them by replacing them with limit values. Automation of this procedure allows not only to improve the accuracy of the simulation results, but also to control the quality of the input data using special counters for the number of changed values ​​for each parameter. If the number of changed values ​​is large enough, for example, more than 10% of all values, this indicates the need to change the standard deviation or adjust the trend of the values ​​of this parameter.

In practice, when building models of cash flows, it is often necessary to take into account the relationship between model parameters in the form of correlation dependencies. Therefore, the ability to specify a correlation is a mandatory element when developing a model. The described model provides for the possibility of setting the correlation in two stages. At the first stage, in an analytical or tabular form, the dependence between the parameters that have a correlation is determined. At the second stage, to set deviations, the analyzed dependence is multiplied by a random variable, the characteristics of which are indicated in the initial data in accordance with the algorithm described above for parameters of the third type.

3.4. Development of a company's cash flow model

The most important characteristics of the cash flow model are the duration of the planning horizon, the length of the calculation step, as well as the moment of bringing the cash flows.

The choice of the planning horizon and the length of the calculation step is determined primarily by the possibility of obtaining high-quality forecasts of the main items of income and expenses of the company. It seems that in Russian conditions the planning horizon for most companies does not exceed four years. In this case, a quarter can be recommended as the length of the calculation step. Then the number of periods in the cash flow model will not exceed seventeen, taking into account the zero period, to which cash flows are usually given. This assumes that all flows occur at the end of the period.

The development of a cash flow model is a creative process that requires taking into account the characteristics of a particular company. At the same time, it is advisable to adhere to the typical structure of the model, according to which cash flows are divided into three groups: operating (flows from current activities), investment (associated with investments in fixed assets and working capital), and financial (associated with servicing the company’s loans). As a final indicator in the considered model, the discounted cash flow for owners is used. An example of the structure of the cash flow model is presented in table 3.4.

Table 3.4. An example of the structure of a company's cash flow model

* "+" - cash inflow; "-" - cash outflow; "=" is the calculation formula, where the numbers in the formula mean the row numbers of the table.

** is not a cash flow, but is used to calculate income tax.

The above structure shows the general logic of building a cash flow model in accordance with financial theory. However, a specific set of income and expense items is individual for each company and depends on the profile of its activities and the characteristics of business processes identified in the course of statistical analysis of the initial data.

In our opinion, the dependence of the model structure on the initial data is of fundamental nature, since, like other stages of the technology for building a forecasting model, the stage of developing a cash flow model should provide the most complete account of the collected information. This can be achieved by applying the top-down principle. In accordance with it, the most generalized model is first built (based on the balance sheet and income statement), which is then detailed to take into account all significant factors, including setting multidirectional trends. When analyzing the company's expense items, it is advisable to use the share of each item in the total amount of expenses of this group as a detailing criterion. For example, when forming corporate expenses, only items that make up at least 5% of corporate expenses are singled out as separate lines, and all other expenses are summarized in one line.

When analyzing a company's revenues (especially if there are dozens of products in its assortment), the problem of grouping products into segments often arises. Here, in addition to the “top-down” principle, it is also necessary to take into account that the formed segments must retain their homogeneity (for more details, see paragraph 2.2).

The implementation of the "top-down" principle increases the versatility of the model building technology, since it allows the use of simulation modeling tools for models of varying degrees of detail, depending on the amount of information available. This feature of the proposed methodological approach opens up opportunities for the active use of forecasting models in external analysis, including by parent companies, as well as banks and other financial institutions (for more details, see Section 4).

3.5. An example of using a company development forecasting model

Let us illustrate the application of the considered model on the example of a company producing two types of products. The planning horizon is two years; Quarter is used as the calculation step.

As can be seen from the initial data (Table 3.5), the volume of sales of the first product is increasing, while sales of the second product tend to decrease. In addition, a number of expenditure items are expected to increase. As a result, the general trend of change in the mathematical expectations of the resulting cash flow of the company by periods is negative. However, the multidirectional trends and the difference in the variances of the key parameters of the model do not allow assessing the variability of cash flows without special tools.

As the simulation results show (Table 3.6, Figure 3.1), although the resulting cash flow is reduced by less than half by the end of the first year, the probability that it will turn out to be negative in the fourth period increases significantly (up to 4%).

Table 3.5. An example of setting initial data for a company development forecasting model

* n – normal distribution; e – empirical distribution k – constant standard deviation; c – constant coefficient of variation.

* * "/" - cash outflow

Table 3.6. The results of the analysis of the company's development prospects

The subsequent acceleration of the decrease in the resulting cash flow of the company leads to an extremely fast, avalanche-like increase in the probability of its negative value up to 50% or more. This feature indicates that the company is able to lose financial stability within a fairly short period of time (in the example under consideration, three quarters).

The ability to assess the dynamics of cash flow and the risk of insolvency is extremely important, since it shows what time period the company's managers have to develop measures to change the identified negative trends. In this example, this period is five quarters.

Rice. 3.1. The dynamics of changes in the mathematical expectation, minimum and maximum of EqCF when analyzing the prospects for the development of the company.

Table 3.7. The results of the impact of the strategy on the company's development prospects

The adaptability of the model, which makes it possible to modify the structure of cash flows, makes it possible to assess the profitability of various development strategies, their impact on changing the risk of a company's insolvency. This can be achieved by including cash flows from new investment projects in the company's development model and taking into account the financial consequences of other management decisions (for example, changes in pricing strategy).

Rice. 3.2. The dynamics of changes in the EqCF of the company, taking into account the release of a new product.

As an example, consider the results of the author's assessment of the investment strategy being developed in the company, which involves the release of a new highly profitable product. As can be seen from Table 3.7 and Figure 3.2, during the first six periods, the company was projected to experience a steady decline in its cash flow to owners (EqCF). At the same time, the probability of negative cash flow increased to 12%, which corresponds to the critical level of risk according to the classification used by the company. As the simulation results showed, the release of a new type of product will increase cash flow over two periods from 5 to 10 million rubles, reduce the risk of negative cash flow from 12 to 1%, and thereby normalize the financial position of the company.

Thus, the use of a forecasting model opens up wide opportunities for companies to predict the dynamics of cash flows and their volatility, which makes it possible to increase the financial stability of the company. The implementation of the forecasting model in the form of a software package based on MS Excel makes its use available to most companies as an effective tool for information support of the strategic management process at the stages of analyzing the position of the company, comparative assessment of the developed development strategies, making investment and financial decisions.

Some other applications of the predictive model

Despite the fact that the main tasks of the forecasting model are to assess the prospects for the development of the company, the profitability of the developed development strategies and the risk of insolvency (discussed in more detail in the previous section), there are a number of other urgent tasks in which the use of the forecasting model can increase the effectiveness of strategic financial management.

Applying predictive models for internal analysis

As the consequences of the global economic crisis have shown, an extremely urgent task for Russian companies is to evaluate the effectiveness of various lending schemes. The forecasting model makes it possible to estimate the maximum debt burden of the company, at which the risk of its insolvency will not go beyond the acceptable values ​​for the owners of the company.

The forecasting model allows you to evaluate the effectiveness of the risk management system in the company. It can be used to evaluate various conditions for insuring the company's key risks. For this, data on the frequency of occurrence of each risk and the probability distribution of the associated damage are used. In the modeling process, when a risk situation arises, the damage is reflected in the form of an additional cash outflow. At the next stage, the model includes cash flows associated with insurance payments and payments in case of risk realization. The model can be used to calculate the total damage from the system of risks and predict their joint impact on the change in the risk of the company's insolvency.

In the financial modeling of the considered tasks, the company's managers have all the completeness of internal information, so the developed cash flow models can be quite detailed, take into account complex relationships between parameters.

Application of forecasting models within the framework of external strategic analysis

At the same time, the forecasting model can also be used for external strategic analysis of the prospects and risks of the company's development.

This is especially relevant when exercising strategic control over subsidiaries that are part of the structure of holdings, financial and industrial groups, state corporations and other organizational associations. For these purposes, more aggregated models can be used that reflect only the most significant factors in the development of subsidiaries.

In addition, the model allows taking into account the prospects for the development of key counterparties (for example, key suppliers and customers) of the company. This possibility is a factor in increasing the stability of the company, especially when concluding long-term contracts, since the bankruptcy of one of the counterparties in some cases carries the risk of interruptions in the production process and may result in significant financial difficulties.

The use of forecasting models can also improve the efficiency of decision-making on mergers and acquisitions, as it allows one to quantify the emerging synergies and changes in the total risk of companies participating in such transactions.

Application of forecasting models in banks and other financial institutions

Cash flow analysis is becoming increasingly important in assessing the risk of insolvency of potential corporate borrowers by banks, especially given the advantages of this method compared to methods for assessing creditworthiness based on accounting data (such as, for example, the Altman criterion). Forecasting cash flows when forming a portfolio of loans balanced in terms of profitability and risk makes it possible to estimate the amount of unforeseen losses on it (which, unlike expected losses, are financed from the bank's own capital). The need for a probabilistic analysis of losses for a portfolio of loans makes it very relevant to use simulation modeling for this purpose, which gives the risk-based company development forecasting model the status of a useful additional credit analysis tool.

The use of forecasting models can also be useful in investment companies, since these models make it possible to take into account the available information more fully and, therefore, to more accurately assess the development prospects of issuing companies compared to using, for example, the P/E multiplier. The implementation of the approach proposed by the author in the spreadsheet environment significantly increases the speed of decision-making and the adaptability of models due to the ease of their adjustment when new factors appear that affect the profitability and risks of the investment portfolio.

It should be noted that forecasting models for the purposes of credit and fundamental investment analysis have significant features associated with the limited initial information, the choice of the planning horizon, and the procedure for calculating the resulting cash flow from the standpoint of banks and investment companies. To improve the accuracy of forecasting in such models, industry forecasts can be actively used.

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As the calculation of Pearson's and Kolmogorov's goodness-of-fit tests showed, the probability that the discrepancy between this empirical distribution and the normal one is explained by random factors is less than 0.001.

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See, for example, Van Horn, J~K., Vakhovich, J.M. (Jr.). Fundamentals of financial management. 11th ed. M.: ID Williams, 2004. S. 454-455.

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For more details, see, for example: Collis Montgomery S.A. Corporate strategy. resource approach. M.: CJSC "Olimp-Business", 2007. S. 25-28.

The residual present value of a portfolio is the remaining amount of expected net cash flows from projects in the portfolio. For more information on the residual present value of the project, see Valdaytsev S.V. Business valuation: textbook. allowance. 2nd ed. M.: TK Velby, Prospect Publishing House, 2004. S. 34.

For more details, see Terentiev N.E. Multi-trend model for forecasting the company's development taking into account risks // Finance and business. 2008. No. 3. pp. 78-92.

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