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.
Acknowledgements
Mai Ngoc Bui acknowledges financial support from the UCL Overseas Research Scholarship. The authors would like to thank Stephan Huckemann for helpful discussions.
Citation
Mai Ngoc Bui. Yvo Pokern. Petros Dellaportas. "Inference for partially observed Riemannian Ornstein–Uhlenbeck diffusions of covariance matrices." Bernoulli 29 (4) 2961 - 2986, November 2023. https://doi.org/10.3150/22-BEJ1570
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