Testing of tempered fractional Brownian motions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913987122167808 |
|---|---|
| author | Macioszek, Katarzyna Sabzikar, Farzad Burnecki, Krzysztof |
| author_facet | Macioszek, Katarzyna Sabzikar, Farzad Burnecki, Krzysztof |
| contents | We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of semi-long range dependence and transient anomalous diffusion. In this framework, we consider three types of TFBMs: two with a tempering factor incorporated into their moving-average representation, and one with a tempering parameter added to the autocorrelation formula. We illustrate their dynamics with the use of quantile lines. Using the proposed methodology, we provide a comprehensive power analysis of the tests. It appears that the tests allow distinguishing between the tempered processes with different Hurst parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Testing of tempered fractional Brownian motions Macioszek, Katarzyna Sabzikar, Farzad Burnecki, Krzysztof Methodology Data Analysis, Statistics and Probability We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of semi-long range dependence and transient anomalous diffusion. In this framework, we consider three types of TFBMs: two with a tempering factor incorporated into their moving-average representation, and one with a tempering parameter added to the autocorrelation formula. We illustrate their dynamics with the use of quantile lines. Using the proposed methodology, we provide a comprehensive power analysis of the tests. It appears that the tests allow distinguishing between the tempered processes with different Hurst parameters. |
| title | Testing of tempered fractional Brownian motions |
| topic | Methodology Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2504.11906 |