Inference for partially observed Riemannian Ornstein-Uhlenbeck diffusions of covariance matrices

Mai Ngoc Bui; Yvo Pokern; Petros Dellaportas

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arXiv · 2104.03193

Inference for partially observed Riemannian Ornstein-Uhlenbeck diffusions of covariance matrices

Mai Ngoc Bui·Yvo Pokern·Petros Dellaportas

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Abstract

We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric positive definite matrices viewed as a differential manifold. We then provide Bayesian inference for discretely observed diffusion processes of covariance matrices based on an MCMC algorithm built with the help of a novel diffusion bridge sampler accounting for the geometric structure. Our proposed algorithm is illustrated with a real data financial application.

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Mai Ngoc Bui, Yvo Pokern, Petros Dellaportas. 2021-04-07. Inference for partially observed Riemannian Ornstein-Uhlenbeck diffusions of covariance matrices. https://arxiv.org/abs/2104.03193

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