TY - JOUR
T1 - Parsimony inducing priors for large scale state–space models
AU - Lopes, Hedibert F.
AU - McCulloch, Robert E.
AU - Tsay, Ruey S.
N1 - Funding Information:
The first author acknowledges partial financial support from FAPESP grant 2018/04156-9 and from CNPq grant 303705/2020-5 .
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/9
Y1 - 2022/9
N2 - 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.
AB - 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.
KW - Bayesian modeling
KW - Conditional heteroscedasticity
KW - Forward filtering and backward sampling
KW - Parallel computing
KW - Shrinkage
KW - Sparsity
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U2 - 10.1016/j.jeconom.2021.11.005
DO - 10.1016/j.jeconom.2021.11.005
M3 - Article
AN - SCOPUS:85120462003
SN - 0304-4076
VL - 230
SP - 39
EP - 61
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1
ER -