Student t-Lévy regression model in YUIMA

ArXiv ID: 2403.12078 “View on arXiv”

Authors: Unknown

Abstract

The aim of this paper is to discuss an estimation and a simulation method in the \textsf{“R”} package YUIMA for a linear regression model driven by a Student-$t$ Lévy process with constant scale and arbitrary degrees of freedom. This process finds applications in several fields, for example finance, physic, biology, etc. The model presents two main issues. The first is related to the simulation of a sample path at high-frequency level. Indeed, only the $t$-Lévy increments defined on an unitary time interval are Student-$t$ distributed. In YUIMA, we solve this problem by means of the inverse Fourier transform for simulating the increments of a Student-$t$ Lévy defined on a interval with any length. A second problem is due to the fact that joint estimation of trend, scale, and degrees of freedom does not seem to have been investigated as yet. In YUIMA, we develop a two-step estimation procedure that efficiently deals with this issue. Numerical examples are given in order to explain methods and classes used in the YUIMA package.

Keywords: Student-t Lévy Process, Simulation Methods, YUIMA Package, High-Frequency Data, Statistical Inference, General Financial Modelling

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced stochastic calculus and statistical estimation for a Lévy process with a heavy-tailed distribution (Student-t), involving Fourier inversion and quasi-likelihood methods, indicating high mathematical density. It also provides practical implementation details within the YUIMA R package, including numerical simulation algorithms and parameter estimation procedures, demonstrating significant empirical and computational focus.

  flowchart TD
    A["Research Goal: Estimation & Simulation<br>Student-t Lévy Regression Model in YUIMA"] --> B{"Problem 1: High-Frequency Simulation"}
    A --> C{"Problem 2: Joint Parameter Estimation"}

    B --> D["Method: Inverse Fourier Transform<br>for Unitary to Arbitrary Time Intervals"]
    C --> E["Method: Two-Step Estimation Procedure<br>Trend & Scale/DoF Sequentially"]

    D --> F["Input: Simulation Parameters<br>Degrees of Freedom, Scale, Length"]
    E --> G["Input: High-Frequency Data<br>Model Driven by t-Lévy Process"]

    F --> H["Computational Process<br>YUIMA Package Implementation"]
    G --> H

    H --> I["Key Findings/Outcomes<br>Effective Simulation via Fourier Transform<br>Efficient Joint Estimation via Two-Step Method"]