Parsimony inducing priors for large scale state–space models
提出一种灵活的先验分布，用于大规模状态空间模型的贝叶斯分析，通过混合四种常见模型实现高维系统的简约性，并应用于S&P 100指数日对数收益率的时变协方差矩阵估计。
State–space models are commonly used in the engineering, economic, and statistical literature. They are flexible and encompass many well-known statistical models, including random coefficient autoregressive models and dynamic factor models. Bayesian analysis of state–space models has attracted much interest in recent years. However, for large scale models, prior specification becomes a challenging issue in Bayesian inference. In this paper, we propose a flexible prior for state–space models. The proposed prior is a mixture of four commonly entertained models, yet achieving parsimony in high-dimensional systems. Here ‘‘parsimony’’ is represented by the idea that, in a large system, some states may not be time-varying. Our prior for the state–space component’s standard deviation is capable to accommodate different scenarios. Simulation and simple examples are used throughout this paper to demonstrate the performance of the proposed prior. As an application, we consider the time-varying conditional covariance matrices of daily log returns of the components of the S&P 100 index, leading to a state–space model with roughly five thousand time-varying states. Our model for this large system enables us to use parallel computing.