Fitting time-varying parameter models via partially noncentered parametrizations
Abstract
Time-varying parameter (TVP) models are widely used to capture evolving relationships but inference is often computationally demanding due to high-dimensional latent states. The efficiency of iterative algorithms depends critically on the choice of latent state augmentation, with centering preferred for genuinely time-varying coefficients and noncentering favored when coefficients are nearly constant. We propose a partially noncentered parametrization that bridges these extremes via dimension-specific working parameters for both location and scale. Optimal working parameters are derived by analyzing EM convergence rates, and an alternating expectation-conditional maximization algorithm is developed to implement the approach. As the convergence rate of mean-field variational Bayes (MFVB) is closely related to EM, we extend the approach to develop partially noncentered MFVB algorithms for the TVP model, placing triple gamma priors on baseline coefficients and process variances to induce shrinkage. Simulations and empirical applications show that the resulting MFVB algorithms yield posterior approximations closer to Markov chain Monte Carlo than conventional centered or noncentered parametrizations. We also develop an efficient solver for the block tridiagonal inverse matrices arising in the proposed algorithms.
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BibTeX
@misc{wang2026fitting,
title = {{Fitting time-varying parameter models via partially noncentered parametrizations}},
author = {Lingjie Wang and Rufeng Liu and Abhinek Shukla and Linda S. L. Tan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33392},
eprint = {2610.33392},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33392},
}
RIS
TY - UNPB
TI - Fitting time-varying parameter models via partially noncentered parametrizations
AU - Lingjie Wang
AU - Rufeng Liu
AU - Abhinek Shukla
AU - Linda S. L. Tan
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33392
UR - https://arxiv.org/abs/2610.33392
AB - Time-varying parameter (TVP) models are widely used to capture evolving relationships but inference is often computationally demanding due to high-dimensional latent states. The efficiency of iterative algorithms depends critically on the choice of latent state augmentation, with centering preferred for genuinely time-varying coefficients and noncentering favored when coefficients are nearly constant. We propose a partially noncentered parametrization that bridges these extremes via dimension-specific working parameters for both location and scale. Optimal working parameters are derived by analyzing EM convergence rates, and an alternating expectation-conditional maximization algorithm is developed to implement the approach. As the convergence rate of mean-field variational Bayes (MFVB) is closely related to EM, we extend the approach to develop partially noncentered MFVB algorithms for the TVP model, placing triple gamma priors on baseline coefficients and process variances to induce shrinkage. Simulations and empirical applications show that the resulting MFVB algorithms yield posterior approximations closer to Markov chain Monte Carlo than conventional centered or noncentered parametrizations. We also develop an efficient solver for the block tridiagonal inverse matrices arising in the proposed algorithms.
ER -