Математические методы и модели микроэкономики
It is proposed the model for computation of the stability ratio of financial and economic indicators, which allows take into account the change depth of the analyzed indicator in time (periodicity, duration and magnitude) and interrelations of its values within the considered time period.
This study provides two models of multiple regressions of graduates of educational institutions of higher education in the Russian Federation. One model is based on the source indicators, and the other - on the principal components. Identified and justified by the benefits of the regression equation, which was built on the components.
In work are considered questions of indicators for economic analysis of activity the company.
Identified problems which the analyst faces at a choice of economic indicators. Presented the opinions of scientists about the essence, functions, and requirements to the indicators. Identified and justified principles of economic indicators for the analysis of the company.
Results can be used in the practice of analytical work at the enterprise.
The task of improving the quality of forecasting returns of financial instruments using multivariate mathematical models: regression models and neural networks was analyzed. To construct a multifactor model of returns used the assumption on the influence of market factors that have a different nature. A linear multivariable regression model was constructed using stepwise inclusion algorithm. The multilayer neural network trained using back-propagation algorithm. The quality of the neural prediction models forecast much higher quality, built with the help of a regression model.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.