Student t-Lévy regression model in YUIMA
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913270322954240 |
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| author | Masuda, Hiroki Mercuri, Lorenzo Uehara, Yuma |
| author_facet | Masuda, Hiroki Mercuri, Lorenzo Uehara, Yuma |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_12078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Student t-Lévy regression model in YUIMA Masuda, Hiroki Mercuri, Lorenzo Uehara, Yuma Computation Statistical Finance Applications 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. |
| title | Student t-Lévy regression model in YUIMA |
| topic | Computation Statistical Finance Applications |
| url | https://arxiv.org/abs/2403.12078 |