Time-dependent shrinkage of time-varying parameter regression models

This article studies the time-varying parameter (TVP) regression model in which the regression coefficients are random walk latent states with time-dependent conditional variances. This TVP model is flexible to accommodate a wide variety of time variation patterns but requires effective shrinkage on the state variances to avoid over-fitting. A Bayesian shrinkage prior is proposed based on reparameterization that translates the variance shrinkage problem into a variable shrinkage one in a conditionally linear regression with fixed coefficients. The proposed prior allows strong shrinkage for the state variances while maintaining the flexibility to accommodate local signals. A Bayesian estimation method is developed that employs the ancilarity-sufficiency interweaving strategy to boost sampling efficiency. Simulation study and an empirical application to forecast inflation rate illustrate the benefits of the proposed approach.