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

TL;DR

This paper proposes a novel interpolation method for numerical series using Fermat-Torricelli points and exponential series, offering an alternative to regression analysis that does not require statistical assumptions.

Contribution

The paper introduces a new interpolation approach based on Fermat-Torricelli points and exponential series, applicable to economic data without normality or independence assumptions.

Findings

Achieves interpolation accuracy comparable to regression analysis.

Does not require normal distribution or independence of errors.

Applicable to economic time series like inflation data.

Abstract

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.