Dynamic shrinkage processes. (28th May 2019)

• Record Type: Journal Article
• Authors: Kowal, Daniel R.; Matteson, David S.; Ruppert, David
• Is Part Of: Journal of the Royal Statistical Society. Volume 81:Number 4(2019)
• Page Start: 781
• Page End: 804
• Publication Date: 2019-05-28
• Subjects: Asset pricing -- Dynamic linear model -- Stochastic volatility -- Time series -- Trend filtering; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12325
• Languages: English
• ISSNs: 1369-7412

Abstract

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.