Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.06343 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917179155283968 |
|---|---|
| author | Majumdar, Sourav Laha, Arnab Kumar |
| author_facet | Majumdar, Sourav Laha, Arnab Kumar |
| contents | We develop diffusion models for time-varying correlation using stochastic processes defined on the unit circle. Specifically, we study Brownian motion on the circle and the von Mises diffusion, and propose their use as continuous-time models for correlation dynamics. The von Mises process, introduced by Kent (1975) as a characterization of the von Mises distribution in circular statistics, does not have a known closed-form transition density, which has limited its use in likelihood-based inference. We derive an accurate analytical approximation to the transition density of the von Mises diffusion, enabling practical likelihood-based estimation. We study inference for discretely observed circular diffusions, establish consistency and asymptotic normality of the resulting estimators, and propose a stochastic correlation model for financial applications. The methodology is illustrated through simulation studies and empirical applications to equity-foreign exchange market data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusion on the circle and a stochastic correlation model Majumdar, Sourav Laha, Arnab Kumar Statistics Theory Mathematical Finance We develop diffusion models for time-varying correlation using stochastic processes defined on the unit circle. Specifically, we study Brownian motion on the circle and the von Mises diffusion, and propose their use as continuous-time models for correlation dynamics. The von Mises process, introduced by Kent (1975) as a characterization of the von Mises distribution in circular statistics, does not have a known closed-form transition density, which has limited its use in likelihood-based inference. We derive an accurate analytical approximation to the transition density of the von Mises diffusion, enabling practical likelihood-based estimation. We study inference for discretely observed circular diffusions, establish consistency and asymptotic normality of the resulting estimators, and propose a stochastic correlation model for financial applications. The methodology is illustrated through simulation studies and empirical applications to equity-foreign exchange market data. |
| title | Diffusion on the circle and a stochastic correlation model |
| topic | Statistics Theory Mathematical Finance |
| url | https://arxiv.org/abs/2412.06343 |