Paper: arXiv 2408.09267

Authors: Sergey Yekimov

Abstract

The use of Fermat-Torricelli points can be an effective mathematical tool for analyzing numerical series that have a large variance, a pronounced nonlinear trend, or do not have a normal distribution of a random variable. Linear dependencies are very rare in nature. Smoothing numerical series by constructing Fermat-Torricelli points reduces the influence of the random component on the final result. The presence of a normal distribution of a random variable for numerical series that relate to long time intervals is an exception to the rule rather than an axiom. The external environment (international economic relations, scientific and technological progress, political events) is constantly changing, which in turn, in general, does not give grounds to assert that under these conditions a random variable satisfies the requirements of the Gauss-Markov theorem.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper attempts an unconventional geometric application of Fermat-Torricelli points to time-series smoothing and risk management, but suffers from major presentation flaws, fragmented formulas, and inadequate empirical backtesting. The empirical section relies on a trivial 11-year dataset of Czech inflation with incomplete calculations, failing to establish practical utility.

Research Flowchart

  flowchart TD
    A[Goal: Reduce Risk in Non-Normal Time Series] --> B[Input: Financial Time Series Data]
    B --> C[Identify Non-Linear Trends & High Variance]
    C --> D[Construct Fermat-Torricelli Points]
    D --> E[Smooth Numerical Series & Filter Noise]
    E --> F[Outcome: Reduced Random Component & Accurate Risk Assessment]

Cited References (4)

  1. Deposit insurance risk portfolio investment policy, management and results in Georgia (2024) — link
  2. Central points and central lines in the plane of a triangle (1994) — link
  3. The value of the inflation index near the values of -1.3% and 5.3% is very unlikely in reality
  4. The forecast of the inflation index based on the use of Fermat-Torricelli points in the range of (0.47; 3.27)%, according to the author, is closer to the real situation

0 of 4 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.