Fractional Gaussian noise: Projections, prediction, norms
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909290132930560 |
|---|---|
| author | Bodnarchuk, Iryna Mishura, Yuliya Ralchenko, Kostiantyn |
| author_facet | Bodnarchuk, Iryna Mishura, Yuliya Ralchenko, Kostiantyn |
| contents | We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Gaussian noise: Projections, prediction, norms Bodnarchuk, Iryna Mishura, Yuliya Ralchenko, Kostiantyn Probability Primary 60G22. Secondary 60G15, 60G25 We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically. |
| title | Fractional Gaussian noise: Projections, prediction, norms |
| topic | Probability Primary 60G22. Secondary 60G15, 60G25 |
| url | https://arxiv.org/abs/2408.09188 |