TAC Method for Fitting Exponential Autoregressive Models and Others: Applications in Economy and Finance

ArXiv ID: 2402.04138 “View on arXiv”

Authors: Unknown

Abstract

There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for the economic science. We present results that completely solve the problem of the best approximation by means of exponential functions and we will be able to determine what kind of data is suitable to be fitted. Data will be approximated using TAC (implemented in the R-package nlstac), a numerical algorithm for fitting data by exponential patterns without initial guess designed by the authors. We check one more time the robustness of this algorithm by successfully applying it to two very distant areas of economy: demand curves and nonlinear time series. This shows TAC’s utility and highlights how far this algorithm could be used.

Keywords: Nonlinear Approximation, Exponential Functions, Time Series Analysis, Nonlinear Curve Fitting, Econometrics, General/Econometrics

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper involves advanced mathematical analysis of exponential approximation with specific theorems and notation (high math), and it demonstrates the algorithm’s robustness using R package implementation and real-world economic data examples (moderate empirical rigor).

  flowchart TD
    A["Research Goal<br>Best approximation<br>by exponential functions"] --> B{"Select Domain"};
    B --> C["Methodology<br>TAC Algorithm via R package nlstac<br>No initial guess needed"];
    B --> D["Data Inputs<br>Economic &<br>Financial Datasets"];
    C --> E{"Apply TAC Process<br>Iterative numerical fitting"};
    D --> E;
    E --> F{"Convergence Check"};
    F -->|Yes| G["Outcomes<br>Robust Parameter Estimation<br>Validated across:<br>Demand Curves & Nonlinear Time Series"];
    F -->|No| E;