A Tractable State-Space Model for Symmetric Positive-Definite Matrices
A Tractable State-Space Model for Symmetric Positive-Definite Matrices
复制标题
对称正定矩阵的易处理状态空间模型
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
C. Carvalho
中科院分区：
文献类型：
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作者：
Jesse Windle;C. Carvalho
状态空间模型的贝叶斯分析包括计算系统参数及其潜在状态的后验分布。当潜在状态在Rn周围徘徊时，有几个众所周知的建模组件和计算工具可以被组合以实现该任务。当潜在状态被约束到R n的严格子集时，这些模型和工具要么受损，要么完全崩溃。状态空间模型的潜在状态是协方差矩阵，出现在nance和克服的挑战，设计听话的模型在约束设置。为此，我们提出了一个状态空间模型，其观测值和潜在状态在对称正定矩阵的流形上取值，并且可以很容易地计算潜在状态和系统参数的后验分布以及过滤分布和一步预测。在nance的上下文中使用该模型，我们展示了如何使用已实现的协方差矩阵作为数据来预测潜在的时变协方差矩阵。这种方法优于因子随机波动率。
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 R n there are several well-known modeling components and computational tools that may be protably combined to achieve this task. When the latent states are constrained to a strict subset of R n these models and tools are either impaired or break down completely. State-space models whose latent states are covariance matrices arise in nance 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-denite matrices and for which one may easily compute the posterior distribution of the latent states and the system's parameters as well as ltered distributions and one-step ahead predictions. Employing the model within the context of nance, 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.
影响因子：
2.1
作者：
Chiriac, Roxana;Voev, Valeri
通讯作者：
Voev, Valeri