Authors
Vygodchikova I.
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Degree
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PhD in Physics & Mathematics, Associate Professor, National Research Saratov State University named after N. G. Chernyshevsky |
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E-mail
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VigodchikovaIY@info.sgu.ru |
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Location
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Saratov |
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Articles
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Estimating the parameters of a multiple linear regression model according to the minimax criterion
In the study of dynamic processes is necessary realistic and objective causal analysis of events.
Such analysis is possible due to application of mathematical and computer simulation methods. Existing
methods of modelling, quantification and forecasting typically require large volume of the original
data, which is not always available, especially when the simulated indicator depends on several
variables, and they underestimate the possibility of extremely rare events that violate distribution pattern
of this indicator. The purpose of this paper — development of a new minimax method estimating
of dynamic patterns for rectangular grid of values of independent variables, mathematical study
of a new method of modeling, the establishment of an effective algorithm, demonstration of application.
Are stated and proved the properties of the solution of the problem which is implementation of
tools modeling technique, that allowed develop an algorithm in the form of step by step instructions,
which is easily implemented in any software environment. In the article demonstrated examples of
implementation of the algorithm, in particular, reviewed its application to assess the dynamic trends
for the purpose of data compression and prediction of missing values in the sample. Proposed a minimax
model of multiple regression and its realization for estimation of parameters of autoregressive
depending. Mathematical justification and obtained the properties of the new model allowed to develop
effective, from the viewpoint of availability of the software implementation in real-time, algorithm.
Read more...
Modeling of time series multi-valued structures based on uniform approximation in the Hausdorff metricThe development of the methodology of time series analysis has been studied by many researchers.
This G. E. P. Box, G. M. Jenkins, N. N. Taleb, S. Johansen, C. A. Sims, A. Yu. Loskutov,
B. P. Bezruchko, V. B. Bayburin, and many others. One of the effective methods of time series
analysis is the criterion of uniform approximation by Chebyshev, which has not been considered in
the literature in relation to multivalued mappings by using the Hausdorff metric. The paper presents
method of analysis and parameters estimation of a mathematical model of multivalued time
series, composed of ranges of values of a certain indicator using as a criterion of optimality the
maximum of the local Hausdorff distances between ranges of values and the values of the approximating
function.
The aim of this work is to develop a mathematical method of modeling the time series which are
represented by ranges, based on the development of the method of uniform approximation of functions
in case of set-valued maps using the Hausdorff metric, and the creation of effective, from the point of
view of availability of hardware and software implementations in real-time, algorithm.
Read more...
Spline approximation of economic data using minimax approach
Adoption of effective management decisions often involves the need to analyze large amounts of heterogeneous,
poorly structured and noisy information. Therefore, urgent task is creation the decision
support system, which allows elaborating rational strategy, even in the face of heterogeneous information,
and unsustainable trend. In article developed numerical method and algorithm of solving the
problem of approximation data by polynomial splines using minimax optimization criterion. By this
algorithm the decision support system for finite number of iterations obtains unambiguous result and
generates rational proposals to the decision maker.
Read more...
Tools of decisions making based on application minimax indicator for interval data of the stock market dynamics
Decision-making process when carrying out transactions with securities is based on the use of mathematical
models that create competitive advantage in the game of trading robots. When using well-known
methods and models for making trading decisions with securities, initial data are subject to smoothing,
as result of which important properties of simulated process can be lost, which significantly reduces
the efficiency of the decision taken by trading system. Taking into account interval data in mathematical
formulation of the problem of decision-making in the stock market allows you to take into account
the amplitude of the change in the price of shares for each day of trading and justify the indicator to
improve the quality of the generated solutions. Authors of the article design a trading system using
as the primary method of decision-making indicator based on the calculation of minimax criterion.
Is executed the implementation of trading robot, which allowed to improve decision-making method
based on moving average and to increase profitability of operations with shares. To demonstrate tools
of decision-making developed in article, computational experiments were carried out on stock market
based at results of trading shares of company «Rossiiskie seti». Investor, using author’s
tools of trade,
increased its capital by 5% per annum compared with method of trading based on the moving average.
Read more...
Toolkit of decisions making about investment of large Russian companies using hierarchical procedure of ranking and minimax approachDeciding making on structure and volume of investment companies should be based on mathematical
models to make reasonable and reliable choice. Because of significant increase in electronic
transactions at stock market, traditional portfolio investment models are no longer applicable due to
need to process large amounts of constantly changing data, so other portfolio risk assessments are required.
In article is offered the approach consisting in application of rating the companies in model
of uniform distribution of the investment risk serving as alternative the model of minimization of risk
H. M. Markowitz. Much attention is paid to rating procedure, which is the author's development and
based on hierarchical analysis procedure of ranked indicators, taking into account their priority. The
stability of author's approach of rating construction on basis the analysis of results of exclusion the
least priority indicator was proved. Computational experiments were performed. In experiments were
used next indicators – output of production and profits of the largest (by output) of the companies of
Russia. Integral rating of companies was compiled, using which calculation the share structure of investment
was performed using the minimax criterion and additional condition on profitability. Author
recommends use the presented tools to compile an investment portfolio of shares the large companies
in Russia.
Read more...
Approximation of life expectancy in Russia based at interval data and minimax modelArticle provides automated processing of interval data on dynamics life expectancy in Russians over a long period of time (more than 100 years). Software product for approximation of dynamic processes in the demographic sphere that occur under unstable trend conditions is developed. Software product is based at the author's model of spline approximation the interval data by linear polynomials. The algorithm of program uses method for finding the moments of joining linear splines using reasonable properties of solving minimax problem for dynamic series whose values are interval data: the lower limit of the interval is fixed life expectancy of men, the upper limit is fixed life expectancy of women. As result of computational experiments, the jump-type curve approximation obtained. The jump-type curve preserves important properties of modeled series and has good approximation properties. The special feature of developed software product is the ability to get an approximating function in a matter of seconds, which has high accuracy and allows you to analyze profile of demographic situation in Russia, taking into account life expectancy of men and women over a long period. Were identified key turning points (mid 20th century and beginning of 21st century, when there was decline in life expectancy of men and his essential distance from a more stable indicator for women), after which dynamics of indicators have shown an increasing trend of both indices and reducing the gap between them. Read more... |
