Development of stochastic forecasting models based on the quantitative interpretation of technical analysis methods Natalia Aleinikova.
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Aleinikova Natalya Alexandrovna. Development of stochastic forecasting models based on quantitative interpretation of technical analysis methods: dissertation ... candidate of physical and mathematical sciences: 05.13.18 .- Voronezh, 2003.- 123 p.: ill. RSL OD, 61 03-1/869-7
Introduction
Chapter 1. Analysis of existing approaches to building predictive models
1.1. Definition, classification and requirements for forecasts
1.2. Analysis of methods for constructing forecast models
1.2.1. Main approaches
1.2.2. Econometric (fundamental) analysis
1.2.3. Technical analysis
1.2.4. Stochastic simulation
1.2.5. Main advantages and disadvantages of forecasting approaches
1.3. Conclusions, setting the goal and objectives of the study
Chapter 2 Building forecast models using technical analysis indicators
2.1. Theoretical justification for the use of technical analysis indicators in a stochastic modeling model
2.1.1. The moving average model and the stages of introducing the TA indicator into the model
2.1.2. Moving Average Model and Moving Average Indicator
2.1.3. Moving Average Model and Exponential Moving Average Indicator
2.1.4. Moving Average Model and Momentum Indicator
2.2. Construction of a conditional-probabilistic indicator model
2.2.1. Approximation of the distribution of conditional probabilities of a random variable A,
2.2.2. Construction of empirical probability distributions of the quantity hn+l
2.2.3. Approximation of an empirical conditional distribution using theoretical laws 54
2.2.4. Using the Normal Distribution to Estimate a Conditional Probability Distribution
2.2.5. Using the Normal and Pareto Distributions to Estimate the Conditional Probability Density Function 57
2.2.6. Using the Pareto and Uniform Distributions in Estimating the Conditional Probability Density Function 63
2.2.7. Formulation of requirements for the scope of the UVIM predictive model
2.3. Findings 66
Chapter 3 Implementing Forecast Models 68
3.1. Description of the technique for checking the performance of forecasting models
3.1.1. Stages of testing the performance of IMSS models
3.1.2. Stages of checking the operability of the UVIM model
3.1.3. Practical verification of the performance of the IMSS model
3.1.4. Brief description of the global commodity futures market
3.1.5. Practical verification of the operability of the UVIM model
3.1.6. Approximation of the empirical conditional distribution using theoretical laws
3.2. Information and analytical subsystem "IS-Trader"
3.2.1. General description of "IS-Trader" 100
3.2.2. Section "Analysis of the situation on the world sugar market and forecast of its development"
3.3. conclusions
Conclusion
Literature
Applications
Main advantages and disadvantages of forecasting approaches
In the general case, a forecast is usually understood as a scientifically based proposition, which is of a probabilistic nature, about the possible states of the object (phenomenon) under study in the future or about the ways and timing of achieving certain goals and results. Forecasting is the process of developing forecasts in order to predict the dynamics of changes in objects (phenomena) in the near or long term.
Let us give the following classification of forecasts, on the basis of which we will more accurately determine the place occupied by our forecast in the future. Forecasts are divided according to the following parameters: Depending on the methodology used a) In a normative forecast, the desired state, goal, result is formulated, which must be achieved in the future. The object of forecasting is the ways, directions of possible development, leading to the realization of the goal; b) Research forecasts are based on the study of trends in the change of the object over time and the distribution of the found dependence on the future. When using the research approach, it is assumed that the elements of the future development of phenomena are embedded in the facts of reality and the laws of the past; c) An integrated forecast combines elements of the previous two approaches; By the nature of the relation of the forecast to the state of the object of forecasting: a) A conditional (active) forecast makes it possible to assess possible directions of development and their consequences, taking into account the influence of exogenous (external) and endogenous (internal, operating within the predicted system) factors; b) An unconditional (passive) forecast characterizes the future development as a result of movement by inertia, the patterns of which are formed in the past and present; According to the degree of spread of prognostic estimates: a) Point forecast describes the possible state of the object with the help of a uniquely established numerical value; b) The interval forecast characterizes the state of the object in the form of a set of numerical values enclosed in a certain interval. The task of building forecast models is quite complicated, since when solving it, it is necessary to take into account the features of the modeled object and the conditions in which the object operates. The paper considers objects whose behavior cannot be predicted in advance, since it depends on many random factors and the main difficulty lies in the impossibility of measuring all these factors, as well as suggesting which of the factors will have the greatest impact at one time or another. Attempts to delve into the cause-and-effect relationships between external factors and the behavior of an object can lead the researcher as far as he likes from a specific change in the state of the object. The task is complicated by the fact that, even having dealt “today” with the reasons that led to a certain state of the object, “tomorrow” there is a risk of getting a completely new reality, where other forces and factors can play a leading role that will create an event series that is not similar to the previous one. The most striking example of such objects are the prices on financial and commodity world exchanges. Let us formulate the initial requirements for forecast models. First, the influence of external factors, which can be very numerous and which cannot always be measured, should be excluded from the model; secondly, to use information about the behavior of the object in previous periods in mathematical forecasting models; thirdly, it is necessary that the model takes into account the uncertainty in the behavior of the object; fourthly, in accordance with the above classification, the forecast must be exploratory, passive, the model must allow interval and point estimates of the predicted values. Let us analyze the main features of the existing and most common approaches to forecasting, highlight the advantages and disadvantages of each approach in terms of the formulated requirements. There are many approaches to predicting the dynamics of objects. Experts try to predict the further development of events, using the mathematical and statistical methods and models proposed by them, exploring patterns, trying to take into account the influence of many different factors that can affect the behavior of an object, and finally, they even resort to intuition. In this paper, only quantitative forecasting methods are considered. The main quantitative methods for constructing forecast models can be divided into three groups: a) Econometric (fundamental) analysis The term "econometrics" was introduced in 1926 by the Norwegian economist and statistician Ragnar Fischer. Literally translated, this term means "measurements in the economy." The main purpose of econometrics is a model description of specific quantitative relationships that exist between the analyzed indicators. Numerous literature is devoted to the description of econometric methods, for example,. b) Technical Analysis (TA) TA is applied in various financial and commodity markets (exchanges) and is based on the hypothesis that market prices are a reflection of the desires and actions of all market participants and all factors (fundamental, political, psychological) affecting the market the price, in fact, is reflected in it. TA methods can be used as a source of additional information for forecasting not only prices, but also other objects (whose characteristics fluctuate over time and have open, close, maximum and minimum states). TA is the least mathematical, but relies on a huge amount of practical material accumulated by graders (market participants) for almost 100 years. Historically, classical TA developed in the following way. Initially, when computer technology did not yet exist in nature, and no one tried to apply mathematical methods to analyze price dynamics due to the complexity of calculations, market participants, especially traders, drew graphs on which they plotted straight lines. Later patterns were found in the ratio of these lines and price charts. This is how trend lines, patterns and figures emerged. Further, there was a need to move away from the straightforwardness of trend lines and models, and traders, also manually, began to calculate average prices, which were successfully used for analysis. And already with the advent of computer technology, it became possible to calculate and apply the methods of oscillatory market analysis.
Moving Average Model and Exponential Moving Average Indicator
Obviously, to build a predictive model that satisfies the requirements formulated in 1.1, it is necessary to combine the features of each of the approaches. To create a suitable predictive model that takes into account uncertainty, you can use existing techniques for building such models in econometrics and stochastic modeling. But at the same time, it is important that the requirement of independence of the predictive output data from the measurement of the values of external random factors is observed. To fulfill this condition, it is proposed to use the stochastic approach as the most suitable one. According to the following requirement - extracting the additional information necessary for the forecast from the very behavior of the predicted value - we will use the indicator methods of technical analysis.
Thus, it is proposed to build a forecasting model within the framework of a stochastic approach using TA indicators. Such a combination of the two approaches seems to be possible in two ways. The first way is to introduce TA indicators into existing stochastic modeling models (for example, a moving average model) and then study the impact that indicators have on the predictive performance of the model. The second way is to create a new model within the probability space (1.4), not related to existing models, using TA indicators as sources of additional information.
It should be noted that, since the model is only an idealization of the real world, in which the relations between real elements that are of interest to the researcher are replaced by suitable relations between mathematical categories, it is necessary to develop a special technique that will be used to test the performance of the model on specific real and test data. , which includes a number of criteria for assessing the quality of the forecast.
To automate the construction of a forecast by combining the methods of stochastic modeling and technical analysis, it is necessary to develop a software package. At the same time, due to the specifics of the methods used, large amounts of statistical information will be required. It is possible to ensure this requirement thanks to the existing information and analytical centers that perform the functions of collecting, storing, processing and issuing information about the current state of the object. It is also important to take into account the fact that the information received about the forecast must be made available, that is, it must be published somewhere. Therefore, the software package must be developed within the framework of the existing information and analytical system that performs the above functions.
From the above analysis of existing approaches and the formulated requirements for forecasting, the following main conclusions can be drawn: a) When building forecasting models, it is necessary to take into account the features of the object being modeled and the conditions in which the object operates. b) A number of requirements are put forward for the forecast model, which consist in its independence from direct measurement of the values of many external random factors, calculation of forecast values based on information about the behavior of the object in the previous period, accounting for uncertainty, and finally, that the forecast obtained using the model should be exploratory, passive, allow interval and point estimates of predicted values. c) An analysis of existing methods for building price forecast models showed that none of the approaches in its pure form leads to the construction of a forecasting model that satisfies the formulated requirements. To achieve the requirements, it is necessary to use a combination of several approaches at once, the most suitable of which are stochastic modeling and indicator technical analysis. d) Combining the two forecasting approaches can be done in two ways. The first way is to introduce TA indicators into existing stochastic modeling models and then study the impact that indicators have on the predictive performance of the model. The second way is to create a new model within the framework of the Kolmogorov probability space, using TA indicators as sources of additional information. e) Building a forecast using a combination of stochastic modeling and technical analysis requires large amounts of statistical information. To ensure this requirement, the existence of information and analytical centers that perform the functions of collecting, storing, processing and issuing information about the current state of the object is necessary. These centers should also ensure the publication of the forecast. f) Within the framework of the existing information and analytical center, it is necessary to develop a software package for the implementation of forecast models. Based on the conclusions, the purpose of the dissertation work is formulated. The aim of the work is to create stochastic forecasting models based on the quantitative interpretation of technical analysis methods and to develop a set of programs as a tool to support decision-making by management subjects. To achieve this goal, it is necessary to solve the following tasks: 1. Theoretically substantiate the use of some indicators of technical analysis in existing models of stochastic modeling. Build a model for predicting the behavior of the object under study based on a stochastic modeling model using technical analysis indicators as a source of additional information. 2. Build a conditional-probabilistic indicator model for predicting the behavior of the object under study that meets the requirements of universality in the use of the types and number of technical analysis indicators, and also develop an algorithm for obtaining predictive estimates using this model.
Using Normal and Pareto Distributions in Evaluating the Conditional Probability Density Function
The paper proposes to use a technique for testing the performance of IMSS forecasting models (Chapter 2, p. 1.) and UWIM (Chapter 2, p. 2) on test and real data, which will be described in general terms below. To present this technique, it is convenient to break the general logical scheme of the study into several stages.
At the first stage, the initial statistical information is collected or formed, as well as the presentation (grouping) of the initial data in a form convenient for further modeling.
The next step is to make sure that the statistical data satisfy the conditions of the model (see Chapter 2, Section 1.6). Indeed, each of the proposed forecasting models has its own area of application. Recall that in the second chapter two assumptions about the behavior of the object were put forward. The first imposed a restriction on the behavior of the object, it was assumed that it was subject to the moving average model. In this regard, there were requirements for the law of price distribution. In practice, we will deal only with random samples from some general population, the empirical characteristics of which may differ from the theoretical characteristics of the entire population. Therefore, it may happen that the predictive model is used for data for which it simply does not apply.
The second assumption did not link the behavior of the object with any known model (although it did not exclude this), but it required that there be sufficiently large statistics on four types of object states - opening, closing, minimum and maximum. Therefore, it is necessary at the second stage of the methodology to check how the sample meets all the initial requirements of the model.
Further, each model included a number of theoretical propositions (Chapter 2, corollaries from Theorems 1,2, Theorem 3, proposals for “gluing” several distribution laws to approximate empirical conditional distributions obtained using the UWIM model), the verification of which in practice will be the third stage of the methodology.
At the fourth stage, it is necessary to specify which values we will consider as a forecast. As a predictive value, you can choose the mathematical expectation, or, if the latter is unknown, the estimate of the mathematical expectation - the sample mean. Increments with maximum frequencies in the sample (sample mode) can also be predictive values. In the case of the IMSS model, when the increments are distributed according to the normal distribution law, due to the symmetry of the law, the mathematical expectation and mode are equal to each other. How much better the forecast obtained with the help of certain data can be judged by going through the next stage of the methodology.
The last (fifth) stage is associated with the need to assess the quality of the forecast obtained using the model. It should be noted that often, to study the quality of the forecast, they are limited to displaying graphs of real and forecast data, and the conclusion about how good the forecast is follows from a simple comparison of these graphs. Such a study is quite subjective. The paper proposes to use a quantitative sign (criterion) of the degree of similarity of the forecast and actual values. At the same time, he must take into account several factors at once, according to which the accuracy of the forecast is estimated (looking at the graph of real and forecast values, researchers and analysts intuitively note these factors). First, it is desirable that the predicted and actual data correlate with each other. That is, if, for example, the actual value moves up, then the predicted value found should also move up. However, the situation shown in Fig. 3.1, when the actual and forecast values, despite the similarity of the directions of their changes, differ significantly in magnitude. Therefore, it is also necessary to take into account the degree of discrepancy between them.
The next factor by which the quality of the forecast is assessed is related to the concept of a confidence interval. The fact is that as a pro Graphs of the movement of forecast and real values. predictive value, you can take a point estimate of the mathematical expectation and a random variable - the sample mean x. But since this estimate is obtained from a sample, it is also a random variable and can differ significantly from the mathematical expectation of the general population. To give an idea of the accuracy and reliability of the x estimate, a confidence interval is built for the mathematical expectation: where y is the confidence probability - the probability that / will cover the unknown value of the mathematical expectation, /?! 32(x],...,xn) - the boundaries of the interval (built on the basis of a sample, they are random variables, D (xj,..., xn) /?2 (xi xn)) are found from the condition that the probability of hitting of the unknown mathematical expectation av 1y is quite large: Obviously, the interval estimate is better, the smaller the length of the confidence interval. And since the boundaries of the confidence interval directly depend on the variance, if it turns out that the variance of the predicted value has decreased after applying the model, then we can assume that using the model improves the quality of the forecast. Based on the foregoing, it is proposed to introduce a vector criterion for assessing the quality of the forecast, which includes three components:
The first component q]f, which is used to study the accuracy of the forecast, is the degree of closeness of the relationship (correlation) between changes in the forecast and real values. To formalize this criterion, you can use a regression analysis indicator, such as the correlation coefficient. But before using this indicator, it is necessary to introduce some additional assumptions about the regression relationship between the predicted and actual values. Since the actual values when testing the model are known to us in advance, using econometric terminology, we can interpret the actual data as explanatory variables, and the predicted values as explanatory variables, while assuming that these variables are related by some dependence y = f(y) + є , for example, linear, which can be described using the formula
Approximation of the empirical conditional distribution using theoretical laws
The most common and convenient way to import goods, including sugar, is to purchase goods on world futures exchanges under futures contracts. A futures contract is a legal obligation to deliver or receive a specified quantity of a specified commodity at an agreed price on a specified date (or days) in the future. A futures contract fixes "now" the price and the terms of a transaction that will take place in the future. The subjects of futures contracts can be agricultural products (sugar, livestock, etc.), crude oil, aluminum, gold, etc., as well as various financial instruments (bills, bonds, currency, etc.). The largest futures exchanges are the Chicago Mercantile Exchange (CME - Chicago Mercantile Exchange), the London International Financial Futures Exchange (LIFFE - London International Financial Futures Exchange), the New York Mercantile Exchange (CSCE or NYMEX - New-York Mercantile Exchange). The popularity of futures exchanges is due to a number of reasons, the most important of which are listed below: a futures exchange is a traditional, century-old commodity market; futures contracts help to avoid the risk of changes in the price of goods; information about futures prices is distributed via the Internet (for example, the Reuters Monitor network); trading on the futures exchange can now be carried out via the Internet (for example, using the Reuters Dealing 2000 and Quotron FX Trader systems). It should be noted that due to its popularity among importers, the futures market has a significant impact on the Russian commodity market. This is expressed, among other things, in the dependence of Russian sugar prices on world futures prices for raw sugar. The price on the domestic Russian sugar market is generally formed by own production and through purchases on international futures exchanges.
The behavior of prices in the futures market, including for sugar, cannot be predicted in advance. Prices on the world sugar market are not stable, constantly fluctuating, and depend on the balance of supply and demand, which is established on the sugar market not according to strict laws, but as a result of competition between market participants. At the same time, even if a “compromise agreement” is reached between the parties, where some market participants always “ask too much”, while others “offer too little” in exchange, it will be very unstable and unpredictable.
But participants in the futures market, such as the state, trading companies, traders, for successful and efficient work, planning, for the correct and competent regulation of the import of goods, in order to obtain the greatest profit, at least partially reduce uncertainty and risk, it is necessary to foresee what situation will develop in the futures market, to be able to qualitatively or quantitatively determine the degree of probability of a particular outcome of the situation. This requires special tools, methods that make it possible to obtain reasonable and as accurate as possible forecasts of the behavior of market prices, timely collected, reliable information about the state of the market. A competent, reasonable forecast reduces the risks of erroneous decisions on the part of market participants.
In countries with developed market economies, and recently in our country (which is associated with an increase in the volume of imports of goods), special information and analytical centers are being created that perform the functions of collecting, storing, processing and issuing information about the current state of commodity markets, necessary for further assessment and forecasting of the state of market entities. Examples of such information and analytical centers in the sugar market are the information system "Russion Sugar" by Stele, the information and analytical system "Informsugar". The data collected, processed and analyzed by these centers are published in the media, as well as on special sites on the Internet. As they develop, in order to support decision-making, such think tanks pay more and more attention to the development of information technologies in the form of economic and mathematical models and methods. Particular attention is paid to the problems of predicting the behavior of the market, market prices. The analysis carried out in showed that forecasting methods in the sugar industry are not sufficiently developed. Let's list the conditions under which the predictive model is built: a) Trades on futures exchanges are held every day except Saturday and Sunday. b) Price information is regularly published in magazines and on the Internet, making it available to all market participants. c) There are special archives in analytical centers on the Internet containing large volumes of data on prices for previous periods, which makes it possible to use statistical methods of information processing. d) Published price data includes high, low, open and close prices, intraday prices, daily prices, weekly averages, monthly averages, etc. Thus, futures prices satisfy all the conditions of the WWIM model given in Chapter 2, paragraph 2.7.
Kozhevnikov, Alexander Sergeevich
In world practice, more than two hundred forecasting methods are used, while in domestic science - no more than twenty. The introduction indicated that the methods of financial forecasting, which are widely used in developed foreign countries, will be considered.
Thus, depending on the type of model used, all forecasting methods can be divided into three large groups (see Figure 1):
Methods of expert assessments, which provide for a multi-stage survey of experts according to special schemes and the processing of the results obtained using economic statistics tools. These are the simplest and most popular methods, the history of which goes back more than one millennium. The application of these methods in practice, usually, is to use the experience and knowledge of trade, financial, production managers of an enterprise or government agency. As a rule, this ensures that the decision is made in the simplest and fastest way. The disadvantage is the reduction or complete absence of personal responsibility for the forecast made. Expert assessments are used not only to predict the values of indicators, but also in analytical work, for example, to develop weight coefficients, threshold values for controlled indicators, etc.
Stochastic Methods, suggesting the probabilistic nature of both the forecast and the relationship between the studied indicators. The probability of obtaining an accurate forecast increases with the increase in the number of empirical data. These methods occupy a leading place in terms of formalized forecasting and vary significantly in the complexity of the algorithms used. The simplest example is the study of sales trends by analyzing the growth rates of sales indicators. Forecasting results obtained by statistical methods are subject to random fluctuations in data, which can sometimes lead to serious miscalculations.
Stochastic Methods can be divided into three typical groups, which will be named below. The choice for forecasting the method of one or another group depends on many factors, including the available initial data.
First situation- the presence of a time series - occurs most often in practice: a financial manager or analyst has at his disposal data on the dynamics of the indicator, on the basis of which it is required to build an acceptable forecast. In other words, we are talking about highlighting a trend. This can be done in various ways, the main of which are simple dynamic analysis and analysis using autoregressive dependencies.
Second situation- the presence of a spatial aggregate - takes place if for some reason there are no statistical data on the indicator or there is reason to believe that its value is determined by the influence of some factors. In this case, multivariate regression analysis can be used, which is an extension of a simple dynamic analysis to a multivariate case.
Rice. 1 . Classification of methods for predicting the financial condition of an enterprise
Third situation- the presence of a spatio-temporal set - takes place when: a) the series of dynamics are insufficient in length to build statistically significant forecasts; b) the analyst intends to take into account in the forecast the influence of factors that differ in economic nature and their dynamics. The initial data are matrices of indicators, each of which represents the values of the same indicators for different periods or for different consecutive dates.
Deterministic Methods, suggesting the presence of functional or rigidly determined relationships, when each value of the factor attribute corresponds to a well-defined non-random value of the resultant attribute. As an example, we can cite the dependencies implemented in the framework of the well-known DuPont factor analysis model. Using this model and substituting into it the forecast values of various factors, such as sales proceeds, asset turnover, the degree of financial dependence, and others, it is possible to calculate the forecast value of one of the main performance indicators - the return on equity ratio.
Another very illustrative example is the profit and loss statement form, which is a tabular implementation of a rigidly determined factor model that links the effective attribute (profit) with factors (sales income, cost level, tax rates, etc.). And at the level of state financial forecasting, the factor model is the relationship between the volume of state revenues and the tax base or interest rates.
Here it is impossible not to mention another group of methods for financial forecasting at the micro level, based on the construction of dynamic simulation models of the enterprise. Such models include data on planned purchases of materials and components, production and sales volumes, cost structure, investment activity of the enterprise, tax environment, etc. The processing of this information within the framework of a single financial model makes it possible to assess the forecast financial condition of the company with a very high degree of accuracy. In reality, such models can only be built using personal computers, which make it possible to quickly perform a huge amount of necessary calculations.
In the process of financial forecasting, specific methods are used to calculate financial indicators, such as mathematical modeling, econometric forecasting, expert assessments, trending and scripting, and stochastic methods.
Math modeling allows you to take into account many interrelated factors that affect the indicators of the financial forecast, choose from several options for the draft forecast the most appropriate for the accepted concept of production, socio-economic development and the goals of financial policy.
econometric forecasting based on the principles of economic theory and statistics: the calculation of forecast indicators is carried out on the basis of statistical estimated coefficients with one or more economic variables acting as forecast factors; allows you to consider the simultaneous change in several variables that affect the performance of the financial forecast. Econometric models describe, with a certain degree of probability, the dynamics of indicators depending on changes in factors that affect financial processes. When constructing econometric models, the mathematical apparatus of regression analysis is used, which gives quantitative estimates of the average relationships and proportions that have developed in the economy during the base period. To obtain the most reliable results, economic and mathematical methods are supplemented by expert assessments.
Method of expert assessments involves the generalization and mathematical processing of assessments of specialist experts on a particular issue. The effectiveness of this method depends on the professionalism and competence of the experts. Such forecasting can be quite accurate, however, expert assessments are subjective, depend on the "feelings" of the expert and are not always amenable to rational explanation.
trend method, which assumes that some groups of income and expenses depend only on the time factor, proceeds from constant rates of change (constant growth rate trend) or constant absolute changes (linear time trend). The disadvantage of this method is ignoring economic, demographic and other factors.
Scenario development does not always come from scientific and objectivity, they always feel the influence of political preferences, preferences of individual officials, investors, owners, but this allows us to assess the consequences of the implementation of certain political promises.
Stochastic Methods assume the probabilistic nature of both the forecast and the relationship between the data used and the forecast financial indicators. The probability of calculating an accurate financial forecast is determined by the amount of empirical data used in forecasting.
Thus, financial forecasting methods differ in terms of costs and volumes of the resulting information provided: the more complex the forecasting method, the greater the costs associated with it and the volume of information obtained with its help.
Forecast Accuracy
The main criteria in evaluating the effectiveness of the model used in forecasting are the accuracy of the forecast and the completeness of the presentation of the future financial condition of the forecasted object. The issue of forecast accuracy is somewhat more complex and requires closer attention. Forecast accuracy or error is the difference between the predicted and actual values. In each specific model, this value depends on a number of factors.
An extremely important role is played by historical data used in the development of a forecasting model. Ideally, it is desirable to have a large amount of data over a significant period of time. In addition, the data used should be "typical" in terms of the situation. Stochastic methods of forecasting, using the apparatus of mathematical statistics, impose quite specific requirements on historical data, in case of non-fulfillment of which the accuracy of forecasting cannot be guaranteed. The data must be reliable, comparable, sufficiently representative for the manifestation of patterns, homogeneous and stable.
The accuracy of the forecast clearly depends on the correct choice of the forecasting method in a particular case. However, this does not mean that only one model is applicable in every case. It is quite possible that in some cases several different models will produce relatively reliable estimates. The main element in any forecasting model is the trend or line of the main trend of the series. Most models assume that the trend is linear, but this assumption is not always reasonable and may adversely affect the accuracy of the forecast. The accuracy of the forecast is also affected by the method used to separate seasonal fluctuations from the trend - addition or multiplication. When using regression methods, it is extremely important to correctly identify the cause-and-effect relationships between various factors and put these relationships into the model.
Before a model can be used to make realistic predictions, it must be tested for objectivity in order to ensure that the predictions are accurate. This can be achieved in two different ways:
The results obtained by the model are compared with the actual values after a certain period of time, when they appear. The disadvantage of this approach is that testing the "impartiality" of the model can take a long time, since the model can only really be tested over a long time period.
The model is built from a truncated set of available historical data. The rest of the data can be used for comparison with the predicted figures obtained using this model. This kind of verification is more realistic, since it actually models the predicted situation. The disadvantage of this method is that the most recent, and therefore the most significant indicators are excluded from the process of generating the original model.
In light of the above regarding model validation, it becomes clear that in order to reduce the expected errors, it is necessary to make changes to an already existing model. Such changes are made throughout the entire period of application of the model in real life. Continuous changes are possible in terms of trend, seasonal and cyclical fluctuations, as well as any causal relationship used. These changes are then verified using the methods already described. Thus, the model design process includes several stages: data collection, development of the initial model, verification, refinement - and again, all over again based on the continuous collection of additional data in order to ensure the reliability of the model.
Types of forecasts
There are three main types of forecast: technological, economic and forecast of sales (demand).
1. Technology Forecasts cover the level of development of scientific and technical progress or technological development in areas that directly affect the production in which the forecast is made. For example, a company producing computers is interested in the prospects for expanding the amount of memory on floppy disks, because. they are additional products for the use of computers, and an enterprise using harmful, toxic substances in its production is interested in developing technologies for waste treatment and disposal.
The development of scientific and technological progress leads to the emergence of new goods and services, and those, in turn, seriously compete with existing enterprises. A well-made forecast will save financial resources, predict the development of new technologies, even if scientific and technological changes have not affected the production of products.
2. Economic forecast allows you to predict the future state of the economy, interest rates and other factors affecting the development of any enterprise. Such decisions depend on the results of the economic forecast as: expansion or reduction of production capacities; conclusion of new contracts; dismissal or hiring of workers, etc.
3. Understanding the real level of demand for the company's products for a specific period in the future gives a forecast of sales. Such a forecast is the basis for planning and conducting economic calculations. Demand is influenced by many factors, which can be taken into account by making a forecast of sales volume (demand). As a basis for the future forecast, such indicators as the level of demand in the previous period, demographic changes, changes in the market shares of industry organizations, the dynamics of the political situation, the intensity of advertising, competitors, etc. are used.
Stochastic modeling is a form of financial modeling involving one or more random variables. The purpose of such modeling is to assess how likely outcomes are within the forecast to predict conditions for different situations. Monte Carlo simulation is one example of a stochastic model; when used to evaluate a portfolio, various simulations of how a portfolio can perform are developed based on the probability distribution of individual stock returns.
TURN OFF "Stochastic Simulation"
Stochastic modeling represents data or predicts outcomes, all of which allow for some degree of unpredictability or randomness. Stochastic modeling is used in many industries around the world, many of which rely on such models to improve business practices or improve profitability. For example, the insurance industry relies heavily on stochastic modeling to predict the future balance sheets of companies. Other industries and areas of research that depend on stochastic modeling include stock investing, statistics, linguistics, biology, and even quantum physics.
Understanding the concept of stochastic modeling
To understand the sometimes confusing concept of stochastic simulation, it is useful to compare it with deterministic simulation. While the former produces many answers, scores, or results, deterministic modeling is the opposite. In deterministic modeling, there is usually only one solution or answer to a problem in most elementary mathematics. Deterministic modeling also typically dictates that there is only one set of specific values. Alternatively, stochastic modeling can be compared to adding variations to a complex mathematical problem to see its effect on the solution. This process is then repeated in several different ways to create a series of solutions.
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Stochastic modeling in the investment world
Stochastic investment models attempt to predict changes in the prices and returns of assets and asset classes such as bonds and stocks over time. In the investment world, stochastic models can be classified in many ways, having different models for single assets and multiple assets. Such modeling is used in most cases for financial planning and actuarial work, which allows investors and traders to optimize asset allocation, as well as asset and liability management.
The implications of stochastic modeling are vast and far-reaching. The importance of being able to look at different outcomes and factor in different variables is unparalleled, and in some industries this can spell success or failure for a company. Because new variables can come into play at any time, and because the number of variables that can have an effect can be high, stochastic models are sometimes run hundreds or even thousands of times, offering potential outcomes for virtually every situation in a business, industry, portfolio, or agency may encounter.
