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-$t$ L\'evy 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 $t$-L\'evy 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-$t$ L\'{e}vy 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.

翻译：本文旨在讨论R语言YUIMA包中由学生t列维过程驱动的线性回归模型的估计与模拟方法，该过程具有恒定尺度参数和任意自由度。此过程在金融、物理、生物学等多个领域均有应用。该模型存在两个主要问题。其一是高频采样路径的模拟问题：实际上，仅定义在单位时间区间上的t-列维增量服从学生t分布。在YUIMA中，我们通过逆傅里叶变换方法解决了这一问题，用于模拟定义在任意长度区间上的学生t列维增量。其二是趋势项、尺度参数与自由度的联合估计问题目前尚未得到充分研究。为此，我们在YUIMA中开发了一种两步估计方法以高效处理该问题。文中给出了数值示例，以说明YUIMA包中使用的相关方法与类。