The Chebyshev Polynomials Of The First Kind For Analysis Rates Shares Of Enterprises

TL;DR

This paper applies Chebyshev polynomials of the first kind to analyze the share price dynamics of eight Czech enterprises, providing a new method that bypasses variance and correlation calculations for non-normal distributions.

Contribution

It introduces a Chebyshev polynomial decomposition approach for analyzing securities' exchange value dynamics without relying on variance or correlation measures.

Findings

Effective analysis of non-normally distributed share data.

Model enables portfolio analysis without variance and correlation.

Applicable to securities with non-normal return distributions.

Abstract

Chebyshev polynomials of the first kind have long been used to approximate experimental data in solving various technical problems. Within the framework of this study, the dynamics of shares of eight Czech enterprises was analyzed by the Chebyshev polynomial decomposition: CEZ A.S. (CEZP), Colt CZ Group SE (CZG), Erste Bank (ERST), Komercni Banka (BKOM), Moneta Money Bank A.S. (MONET), Photon (PENP), Vienna insurance group (VIGR) in 2021. An investor, when making a decision to purchase a security , is guided largely by an heuristic approach . And variance and correlation are not observed by human senses. The vectors of decomposition of time series of exchange values of securities allow analyzing the dynamics of exchange values of securities more effectively if their dynamics does not correspond to the normal distribution law. The proposed model allows analyzing the dynamics of the exchange value of a securities portfolio without calculating variance and correlation. This model can be useful if the dynamics of the exchange values of securities does not obey, due to certain circumstances, the normal law of distribution.