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

ArXiv ID: 2307.08465 “View on arXiv”

Authors: Unknown

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.

Keywords: Chebyshev polynomials, time series decomposition, portfolio dynamics, distribution laws, heuristic approach, Equities

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper uses Chebyshev polynomials and linear algebra for time series decomposition, representing moderate mathematical complexity, but the empirical testing is limited to analyzing eight stocks in 2021 with no backtests, transaction costs, or implementation details.
  flowchart TD
    A["Research Goal: Analyze Enterprise Share Dynamics<br>Using Chebyshev Polynomials"] --> B{"Methodology: Chebyshev Polynomial Decomposition"}
    B --> C["Data Input: Daily Share Prices of 8 Czech Enterprises<br>CEZP, CZG, ERST, BKOM, MONET, PENP, VIGR, PHOTON (2021)"]
    C --> D["Computational Process: Apply Chebyshev Polynomials<br>to Time Series Decomposition"]
    D --> E{"Distribution Analysis"}
    E -- Non-Normal Distribution --> F["Key Finding: Effective Dynamic Analysis<br>Without Variance/Correlation"]
    E -- Normal Distribution --> G["Alternative: Standard Statistical Methods"]
    F --> H["Outcome: Heuristic Investment Model<br>for Securities Portfolio Dynamics"]
    G --> H