- Bayesian Anal.
- Volume 9, Number 4 (2014), 759-792.
A Tractable State-Space Model for Symmetric Positive-Definite Matrices
The Bayesian analysis of a state-space model includes computing the posterior distribution of the system’s parameters as well as its latent states. When the latent states wander around there are several well-known modeling components and computational tools that may be profitably combined to achieve this task. When the latent states are constrained to a strict subset of these models and tools are either impaired or break down completely. State-space models whose latent states are covariance matrices arise in finance and exemplify the challenge of devising tractable models in the constrained setting. To that end, we present a state-space model whose observations and latent states take values on the manifold of symmetric positive-definite matrices and for which one may easily compute the posterior distribution of the latent states and the system’s parameters as well as filtered distributions and one-step ahead predictions. Employing the model within the context of finance, we show how one can use realized covariance matrices as data to predict latent time-varying covariance matrices. This approach out-performs factor stochastic volatility.
Bayesian Anal., Volume 9, Number 4 (2014), 759-792.
First available in Project Euclid: 21 November 2014
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Windle, Jesse; Carvalho, Carlos M. A Tractable State-Space Model for Symmetric Positive-Definite Matrices. Bayesian Anal. 9 (2014), no. 4, 759--792. doi:10.1214/14-BA888. https://projecteuclid.org/euclid.ba/1416579176
- Related item: Roberto Casarin, Comment on Article by Windle and Carvalho. Bayesian Anal., Vol. 9, Iss. 4 (2014) 793–804.
- Related item: Catherine Scipione Forbes, Comment on Article by Windle and Carvalho. Bayesian Anal., Vol. 9, Iss. 4 (2014) 805–808.
- Related item: Enrique ter Horst, German Molina, Comment on Article by Windle and Carvalho. Bayesian Anal., Vol. 9, Iss. 4 (2014) 809–819.
- Related item: Jesse Windle, Carlos M. Carvalho (2014). Rejoinder. Bayesian Anal., Vol. 9, Iss. 4 (2014) 819–822.