Parsimony Inducing Priors for Large Scale State-Space Models

Abstract

State-space models are commonly used in the engineering, economic, and statistical literatures. 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 achieves parsimony in high-dimensional systems. Here “parsimony” is represented by the idea that in a largesystem, some states may not be time-varying. Simulation and simple examples are used throughout to demonstrate the performance of the proposed prior. As an application, we consider the time-varying conditional covariance matrices of daily log returns of 94 components of the S&P 100 index, leading to a state-space model with 94×95/2=4,465 time-varying states. Our model for this large system enables us to use parallel computing.