Simulating Continuous-Time Autoregressive Moving Average Processes Driven By p-Tempered α-Stable Lévy Processes
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914925633339392 |
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| author | Massing, Till |
| author_facet | Massing, Till |
| contents | We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable Lévy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of Ornstein-Uhlenbeck processes. However, unlike Ornstein-Uhlenbeck processes with a tempered stable driver (see, e.g., Qu et al. (2021)) exact transition probabilities for higher order CARMA processes are not explicitly given. Therefore, we follow the sample path generation method of Kawai (2017) and approximate the driving tempered stable Lévy process by a truncated series representations. We derive a result of a series representation for ptempered α-stable distributions extending Rosiński (2007). We prove approximation error bounds and conduct Monte Carlo experiments to illustrate the usefulness of the approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simulating Continuous-Time Autoregressive Moving Average Processes Driven By p-Tempered α-Stable Lévy Processes Massing, Till Probability We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable Lévy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of Ornstein-Uhlenbeck processes. However, unlike Ornstein-Uhlenbeck processes with a tempered stable driver (see, e.g., Qu et al. (2021)) exact transition probabilities for higher order CARMA processes are not explicitly given. Therefore, we follow the sample path generation method of Kawai (2017) and approximate the driving tempered stable Lévy process by a truncated series representations. We derive a result of a series representation for ptempered α-stable distributions extending Rosiński (2007). We prove approximation error bounds and conduct Monte Carlo experiments to illustrate the usefulness of the approach. |
| title | Simulating Continuous-Time Autoregressive Moving Average Processes Driven By p-Tempered α-Stable Lévy Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2408.15081 |