Dynamic Shrinkage Processes
提出一类新的动态收缩过程，用于贝叶斯时间序列和回归分析，在保留马蹄先验等全局-局部先验的优良收缩性质的同时，提供局部自适应性，并通过Pólya-gamma尺度混合实现高效吉布斯采样。应用于Twitter CPU数据的不规则曲线拟合和Fama-French五因子资产定价模型的时变参数分析。
Summary We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods.