Fictitious Variables Research Articles

Модели векторной авторегрессии в прогнозировании инфляционных процессов на региональном уровне (на примере Еврейской автономной области)

The paper presents the stages of constructing a vector autoregression model (VAR model) for forecasting inflation at the regional level, and a short-term inflation forecast for the Jewish Autonomous Region. For this purpose, a selection of possible indicators for the VAR model has been singled out, and the need for their use has been economically justified. It has also been proved that it is necessary to use fictitious variables to eliminate the influence of identified shocks in the dynamics of inflation. The resulting VAR model has been recognized as sound after conducting the necessary econometric tests. The model has been verified. It is worth noting that the developed VAR model is suitable only for the study of the selected subject of the Russian Federation, since each region of Russia has its own uniqueness. The selection of indicators should be singled out individually for each territory. At the same time, the algorithm for constructing a forecasting model is universal and can be applied to various territories. It has been concluded that it is important to build an inflation forecast, since its impact must be taken into account in financial planning by absolutely all economic agents at all hierarchical levels: government, business, and the public. The views expressed herein are solely those of the authors. The content and results of this research should not be considered or referred to in any publications as the Bank of Russia’s official position, official policy, or decisions. Any errors in this document are the responsibility of the authors. All rights reserved. Reproduction is prohibited without the authors’ consent.

Вибір економетричного інструментарію при побудові скорингової моделі на основі фіктивних змінних

The aim of the study is to select adequate econometric instruments for building a scoring model on a specific array of initial data, which contains the vast majority of fictitious variables. Despite a significant number of developments devoted to the construction of scoring models, a universal method allowing to obtain a highly efficient classifier for any data has not been identified. Therefore, the task of selection of the best method for building a scoring model remains relevant, depending on the characteristics of the available data. The most successful approach when selecting a model for solving the problem of binary classification is the use of several types of econometric models and the choice of the best of them according to the results of classification. In the presented study, the following types of models were applied: discriminant model, logit and probit regressions, and polynomial logistic regression. Training samples with different structure were used. Comparison of all obtained models allows us to conclude that polynomial logistic regression is preferable in this case. This model demonstrates high classification rates for all introduced object classes and has an important advantage compared to models that make a binary selection. The advantage of polynomial logistic regression is also the possibility of selecting in each case a convenient scale for dividing borrowers into more than two classes and determining the level of probability of reliability of the borrower acceptable for its own conditions, at which it should be assigned to one of the selected classes. Prospects for further research in this direction are the use of machine learning methods that will be able to use ensembles of the best of the considered models. In addition, the proposed models can be used in solving similar problems in other spheres of economic activity.

ЭКОНОМЕТРИЧЕСКИЙ АНАЛИЗ ОБЪЕМОВ ЭКСПОРТА КИТАЯ

The paper analyzes the value volumes of China's exports for 2011-2021 by constructing an econometric model of a time series. The polynomial equation of the trend of the third degree is constructed by introducing fictitious variables. The result of the work is a forecast for 2022

ЭКОНОМЕТРИЧЕСКОЕ МОДЕЛИРОВАНИЕ ОБЪЕМОВ ЗАРАБОТНОЙ ПЛАТЫ В РОССИЙСКОЙ ФЕДЕРАЦИИ

The article econometric analysis of the volume of average nominal accrued wages in the Russian Federation for 2018-2021. Based on quarterly data a multiplicative model of a time series is constructed. The resulting model served as the basis for calculating the forecast of wage values for the 1st half of 2022. To improve the quality of forecasting, the method of introducing fictitious variables was used.

Application of Election Functions to Estimate the Number of Monotone Self-Dual Boolean functions

One of the problems of modern discrete mathematics is R. Dedekind problem on the number of monotone boolean functions. For other precomplete classes, general formulas for the number of functions of the classes had been found, but it has not been found so far for the class of monotone boolean functions. Within the framework of this problem, there are problems of a lower level. One of them is the absence of a general formula for the number of boolean functions of intersection $MS$ of two classes --- the class of monotone functions and the class of self-dual functions. In the paper, new lower bounds are proposed for estimating the cardinality of the intersection for both an even and an odd number of variables. It is shown that the election function of an odd number of variables is monotone and self-dual. The election function of an even number of variables is determined. Free election functions, which are functions with fictitious variables similar in properties to election functions, are introduced. Then the union of a set of election functions and a set of free election functions is considered, and the cardinality of this union is calculated. The resulting value of the cardinality is proposed as a lower bound for $|MS|$. For the class $MS$ of monotone self-dual functions of an even number of variables, the lower bound is improved over the bounds proposed earlier, and for functions of an odd number of variables, the lower bound for $|MS|$ is presented for the first time.

Market-based pricing for road freight transportation

The specifics of market pricing in the Russian road freight transport market by means of correlation and regression analysis have been studied. Statistically significant factors have been highlighted, and mathematical models have been constructed. The influence of fictitious variables (body type) that improve the quality of the calculated values has been noted. Regression equations useful for determining the average market value of tariffs have been drawn up, which, when compared to actual tariffs, may indicate the adequacy of freight transactions. The results of transport companies registered in the Krasnodar region have been considered. A differentiated approach has been justified, requiring enterprises to be divided into revenue growth groups in order to identify differences in profitability and its sustainability. The limitations and shortcomings of the mathematical model, which do not allow us to make an unambiguous conclusion about the unprofitable and low-margin nature of the industry, have been considered. Areas for future research have been suggested.

Agriculture Land Price Setting Systems, and Possible Directions for Their Updating

The aim of this article is to assess the effect of the applied land valuation system on the price of land, and as a consequence of the implied links to compare the valuation of soil units in Slovakia and the Czech Republic. In order to fulfil this objective, an econometric approach was chosen in the form of a hedonic price model, whereby the heteroscedastic corrected linear regression model was specifically applied. The estimated model shows a very high explanatory ability, together with a high parametric significance for most fictitious variables (land characteristics), and at the same time also fulfils the theoretical and logical consistency of general assumptions. From the results, it is evident that, in the case of Slovakia, ESEU [evaluated soil ecological unit] valuation is affected primarily by the climatic region and the main soil unit. When comparing the results of the effect of individual input factors on the price of land in the Czech Republic and Slovakia, it can be stated that the results are slightly different in the effect of certain factors. The characteristics of soils located in warm climatic regions with a valuable soil type of chernozem and low slope are significant and positively intensive factors.

Cryptographic strength investigation of the algorithm for generating pseudorandom sequences based on a blender

Aim. The purpose of the article is to study the cryptographic strength characteristics of Boolean functions used in the blender algorithm. This algorithm is designed for information security tasks as part of a pseudorandom sequence generator. Methods. The methods of cryptographic Boolean functions theory, the methods of analysis and comparison were used in the work. Results. The general features of the blender Boolean functions are formulated. To assess their cryptographic strength, a computational study of compliance with criteria such as balancedness, algebraic degree, the presence of fictitious variables, the absence of linear structures, correlation immunity, high nonlinearity, avalanche criterion, etc. was performed. A comparison is made with similar results for Boolean functions that are part of nonlinear s-blocks of known cryptographic algorithms. Conclusions. The ability to adjust the blender dimension to obtain blocks of the desired size, forming the output sequence, allows increasing the values of some characteristics of Boolean functions cryptographic strength. It is detected that some cryptographic strength indicators of the Boolean blender functions (balancedness, nonlinearity and global avalanche characteristic) have asymptotic regularities of behavior. The results of the study makes it possible to consider the level of cryptographic strength of the blender Boolean functions acceptable for use in cryptographic protection systems.

The BDF3/EP3 Scheme for MBE with No Slope Selection is Stable

We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in time with implicit treatment of the surface diffusion term. The nonlinear term is approximated by a third order explicit extrapolation (EP3) formula. We exhibit mild time step constraints under which the modified energy dissipation law holds. We break the second Dahlquist barrier and develop a new theoretical framework to prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional result for third order BDF methods applied to the MBE models without introducing any stabilization terms or fictitious variables. A novel theoretical framework is also established for the error analysis of high order methods.

Primena linearnog programiranja na standardni problem maksimuma u transportu

The paper presents the analysis of the transport plan by applying the geometric interpretation of linear programming, dual approach and simplex method to the optimization of the transport plan. The goal is to optimize the transport plan from the aspect of choosing the type of transport task, type and scope of engagement of transport means, in order to maximize the functions of the goal that represents the earnings. The approach to analysis is illustrated by a characteristic task that is solved in the paper in the described way. The main difference between this and the tasks analyzed so far is that the imposed restrictions represent a system of inequalities which, by introducing fictitious variables, is transformed into a system of equations to which the standard maximum problem is applied. The benefit of this approach is a simpler but also more comprehensive approach to the analysis of the transport plan. It is especially suitable for relatively small transport systems when there are a number of limitations and where it is not convenient to buy and use software packages. The emphasis in the paper is on maximizing earnings while meeting the imposed limits. The analysis yielded identical results in all three ways.

On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations

We discuss the existence issue to an optimal control problem for one class of nonlinear elliptic equations with an exponential type of nonlinearity. We deal with the control object when we cannot expect to have a solution of the corresponding boundary value problem in the standard functional space for all admissible controls. To overcome this difficulty, we make use of a variant of the classical Tikhonov regularization scheme. In particular, we eliminate the PDE constraints between control and state and allow such pairs run freely by introducing an additional variable which plays the role of “compensator” that appears in the original state equation. We show that this fictitious variable can be determined in a unique way. In order to provide an approximation of the original optimal control problem, we define a special family of regularized optimization problems. We show that each of these problems is consistent, well-posed, and their solutions allow to attain an optimal solution of the original problem as the parameter of regularization tends to zero. As a consequence, we prove the existence of optimal solutions to the original problem and propose a way for their approximation.

Formula omitted]-Reduction and relative equilibria for a radial axisymmetric intermediary model for roto-orbital motion

A geometrical approach to a radial intermediary model for an axisymmetric rigid body in roto-orbital motion is presented. The presence of symmetries enables a well-suited formulation by choosing action–angle type variables. Singularities associated with the angles are avoided by introducing extra fictitious variables and performing a symplectic transformation leading to a global, quaternionic double-chart. Then, making use of the SO(3) and T4 symmetry of our model, a full reduction process by stages is carried out, which in combination with the constrained dynamics related to the fictitious variables, leads to a 1-DOF reduced-constrained system. Our program includes a parametric analysis of relative equilibria and a complete description of the fibers in the reconstruction of the reduced system.

MODELING THE LEVEL OF COMPETITIVENESS OF INSURANCE COMPANIES

In the article reviewed the necessity of assessing the level of competitiveness of insurance companies. Identified factors that aff ect competitiveness and insurers activity taking into account them in econometric models. By means of coefficients of regression of fictitious variables factors that have a signifi cant impact on the insurance company's competitiveness: payments, gross premiums are determined. We combine all insurance companies in a single set and estimate the regression with diff erentiated coefficients, respectively, forming the fictitious variables of the slope and intersection. According to the position of the insurance company in the rating, we introduce the following fictitious variables: 1 — for an insurance company with a high level of insurance payments; 0 — for insurance companies with insufficient level of insurance payments. A multi-factor regression model and a variance analysis and their comparison are constructed that are statistically significant and adequate. The model is checked for absence of autocorrelation, and can be used as predicted and to assess the state of the insurance company in the insurance market.

Post and Jablonsky Algebras of Compositions (Superpositions)

There are two algebras of compositions, Post and Jablonsky algebras. Definitions of these algebras was very simple. The article gives mathematically precise definition of these algebras by using Mal’cev’s definitions of the algebras. A. I. Mal’cev defined pre-iterative and iterative algebras of compositions. The significant extension of pre-iterative algebra is given in the article. Iterative algebra is incorrect. E. L. Post used implicitly pre-iterative algebra. S. V. Jablonsky used implicitly iterative algebra. The Jablonsky algebra has the operation of adding fictitious variables. But this operation is not primitive, since the addition of fictitious variables is possible at absence of this operation. If fictitious functions are deleted in the Jablonsky algebra then this algebra becomes correct. A natural classification of closed sets is given and fictitious closed sets are exposed. The number of fictitious closed sets is continual, the number of essential closed sets is countable.

Fiscal policy in raw materials economics: the role of the budget and the sovereign wealth funds

The peculiarities of fiscal policy of the countries exporting raw materials have been researched, and the «best practices» of anti-cyclical regulation based on the rule of fiscal policy have been analyzed, in particular. Using the OLS method for the unbalanced spatial-temporal sample of 15 annual data from Latin America, Southeast Asia and the former Soviet Union countries (plus Turkey and South Africa), the impact of budget balances (taking into account the time trend) on GDP growth rates (%), inflation (%), nominal and real interest rates (%), investments (% of GDP), savings (% of GDP), current account balances (% of GDP), as well as the share of high-tech exports in the total volume of export of industrial products (%) has been empirically estimated. Individual characteristics of peculiar countries have been taken into account using the appropriate fictitious variables. The constructivism of countercyclical fiscal policy as a factor in lowering the interest rate, increasing savings and improving the current account balance, which should facilitate stabilization policy in the commodity-oriented economy, has been confirmed. It has been noted, that the creation of sovereign wealth funds is a prerequisite for the implementation of the fiscal policy rules. It has been established, that the efficiency of government expenditures as a factor of long-term economic growth depends on the institutional factors quality.

Wagner’s Law, Public Employment, and Spanish Regions

Abstract Following Peacock and Musgrave’s rediscovery of Wagner’s Law, the latter became a standard tool used in research on the relationship between growth of public spending and the factors by which it is influenced. However, conventional empirical tests are based on a specification error related to Wagner’s definition of the public sector, which he considered in its totality, including public companies. The present article attempts to correct this error and obtain an approximation to the size of the public sector by considering public employment as a whole, both in public administrations and services and in public companies. To this end, panel data for the Spanish autonomous regions are used in addition to data for the overall public sector. The empirical test is performed utilizing cointegration techniques and unit roots in panel data. Similarly, the possibility of structural breaks in the data is taken into consideration and they are estimated using fictitious variables. JEL classifications: H11; H50; E62 Keywords: public employment; gross domestic product; unit root; cointegration; panel data

ОЦІНКА ІНДИКАТОРІВ ФОРМУВАННЯ ЕКОНОМІКИ ЗНАНЬ: НА ПРИКЛАДІ ПОЛЬЩІ ТА УКРАЇНИ

The macroeconomic indicators that characterize the process of the economic system of the state to such a model of the economy, which is based on knowledge have been researched in the article. The essence of knowledge as an economic resource, their multi-characteristic, and impossibility to equate to a single unit of measurement has been determined. The essence, main characteristics, and factors that ensure the formation of the knowledge economy in modern conditions have been revealed. Several indicators have been identified that in one way or another reflect the potential of the state to build a knowledge economy. The role of key social institutions in the process of transition to the knowledge economy is described. Emphasis has been placed on the key role of educational institutions as the main centers of knowledge generation and transfer in the economy. The most common methods of analysis of the formation of the knowledge economy and assessment of the value of knowledge as an independent economic resource in the economy have been analyzed. The method of the research of knowledge economy using the economic and mathematical device, in particular, the regression analysis for research of influence of dynamics of the cost of the created knowledge expressed in volume of investments in research and innovative activity, on dynamics of the basic macroeconomic indicators (GDP, unemployment, financial results) objects of management). Also, to obtain more accurate results, with the help of fictitious variables in the study process the regional aspect has been included and the role of individual regions in the formation of the knowledge economy of the state has been identified. The expediency of using economic and mathematical methods of analysis of the process of knowledge economy formation as the most accurate and specific tools to investigate the relationship between existing knowledge in economics and economic performance of both individuals and the economic system as a whole has been substantiated.

Smoothed Biasing Forces Yield Unbiased Free Energies with the Extended-System Adaptive Biasing Force Method.

We report a theoretical description and numerical tests of the extended-system adaptive biasing force method (eABF), together with an unbiased estimator of the free energy surface from eABF dynamics. Whereas the original ABF approach uses its running estimate of the free energy gradient as the adaptive biasing force, eABF is built on the idea that the exact free energy gradient is not necessary for efficient exploration, and that it is still possible to recover the exact free energy separately with an appropriate estimator. eABF does not directly bias the collective coordinates of interest, but rather fictitious variables that are harmonically coupled to them; therefore is does not require second derivative estimates, making it easily applicable to a wider range of problems than ABF. Furthermore, the extended variables present a smoother, coarse-grain-like sampling problem on a mollified free energy surface, leading to faster exploration and convergence. We also introduce CZAR, a simple, unbiased free energy estimator from eABF trajectories. eABF/CZAR converges to the physical free energy surface faster than standard ABF for a wide range of parameters.

A family of classes of functions closed with respect to a strengthened superposition operation

The paper concerns the operation of binary superposition determined for the k-valued logic functions (k = 2m, m ≥ 2) on the basis of their representation in the binary number system. A description of the set of classes containing only functions taking not more than two values and closed under the operations of binary superposition and addition of fictitious variables is given.

Classification of closed sets of functions in multi-valued logic

Using Mal’cev’s preiterative algebra (iterative algebra is not sound) we construct in the first time the natural classification of closed sets of functions in multi-valued logic: every closed set belongs only one class and the classes are disjoint. All contemporary papers construct only intersecting classes. We confirm Post’s thesis that multi-valued logic does not contain anything special in compare with 2-valued logic. There are non-fictitious and fictitious closed sets. The number of non-fictitious closed sets is countable and the number of fictitious closed sets is continuum. This is natural since number of fictitious objects in every theory is very much in comparison with non-fictitious objects. Fictitious closed sets are useless for classification of functions of logic like fictitious variables are useless for calculation of function. Non-fictitious closed sets can have singleton bases. Any fictitious closed set is a join of non-fictitious closed sets and has only multi-membered basis. This is used for classification of closed sets. The class U0 contains closed sets without basis. A class Um does not contain closed sets with (m 1)-membered bases but contains closed sets with m-membered bases. All the classes are countable. The class Uw contains closed sets with infinite-membered bases. The class is continuum. We construct only the upper level of classification since fictitious closed sets need not have more levels. Only class U1 of non-fictitious closed sets must have more detail classification. But contemporary papers deal with useless fictitious closed sets instead of very important non-fictitious.