Yekimov Sergey | Searcharxiv

arXiv2023

Interpolation of numerical series by the Fermat-Torricelli point construction method on the example of the numerical series of inflation in the Czech Republic in 2011-2021

The use of regression analysis for processing experimental data is fraught with certain difficulties, which, when models are constructed, are associated with assumptions, and there is a normal law of error distribution and variables are statistically independent. In practice , these conditions do not always take place . This may cause the constructed economic and mathematical model to have no practical value. As an alternative approach to the study of numerical series, according to the author, smoothing of numerical series using Fermat-Torricelli points with subsequent interpolation of these points by series of exponents could be used. The use of exponential series for interpolating numerical series makes it possible to achieve the accuracy of model construction no worse than regression analysis . At the same time, the interpolation by series of exponents does not require the statistical material that the errors of the numerical series obey the normal distribution law, and statistical independence of variables is also not required. Interpolation of numerical series by exponential series represents a "black box" type model, that is, only input parameters and output parameters matter.

econ.EM↗

arXiv2023

Smoothing of numerical series by the triangle method on the example of hungarian gdp data 1992-2022 based on approximation by series of exponents

In practice , quite often there is a need to describe the values set by means of a table in the form of some functional dependence . The observed values , due to certain circumstances , have an error . For approximation, it is advisable to use a functional dependence that would allow smoothing out the errors of the observation results. Approximation allows you to determine intermediate values of functions that are not listed among the data in the observation table. The use of exponential series for data approximation allows you to get a result no worse than from approximation by polynomials In the economic scientific literature, approximation in the form of power functions, for example, the Cobb-Douglas function, has become widespread. The advantage of this type of approximation can be called a simple type of approximating function , and the disadvantage is that in nature not all processes can be described by power functions with a given accuracy. An example is the GDP indicator for several decades . For this case , it is difficult to find a power function approximating a numerical series . But in this case, as shown in this article, you can use exponential series to approximate the data. In this paper, the time series of Hungary's GDP in the period from 1992 to 2022 was approximated by a series of thirty exponents of a complex variable. The use of data smoothing by the method of triangles allows you to average the data and increase the accuracy of approximation . This is of practical importance if the observed random variable contains outliers that need to be smoothed out.

econ.EM↗