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December 2014 A Tractable State-Space Model for Symmetric Positive-Definite Matrices
Jesse Windle, Carlos M. Carvalho
Bayesian Anal. 9(4): 759-792 (December 2014). DOI: 10.1214/14-BA888


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 Rn 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 Rn 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.


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Jesse Windle. Carlos M. Carvalho. "A Tractable State-Space Model for Symmetric Positive-Definite Matrices." Bayesian Anal. 9 (4) 759 - 792, December 2014.


Published: December 2014
First available in Project Euclid: 21 November 2014

zbMATH: 1327.62170
MathSciNet: MR3293953
Digital Object Identifier: 10.1214/14-BA888

Rights: Copyright © 2014 International Society for Bayesian Analysis


Vol.9 • No. 4 • December 2014
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