Diffusion on the circle and a stochastic correlation model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917179155283968 |
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| 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 |
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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 |