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  • 标题:A Tractable State-Space Model for Symmetric Positive-Definite Matrices
  • 本地全文:下载
  • 作者:Jesse Windle ; Carlos M. Carvalho
  • 期刊名称:Bayesian Analysis
  • 印刷版ISSN:1931-6690
  • 电子版ISSN:1936-0975
  • 出版年度:2014
  • 卷号:9
  • 期号:4
  • 页码:759-792
  • DOI:10.1214/14-BA888
  • 语种:English
  • 出版社:International Society for Bayesian Analysis
  • 摘要: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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