Dynamic Shrinkage Priors for Large Time-varying Parameter Regressions using Scalable Markov Chain Monte Carlo Methods

Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain Monte Carlo (MCMC) methods mean their use is limited to the case where the number of predictors is not too large. In light of these two concerns, this paper proposes a new dynamic shrinkage prior which re ects the empirical regularity that TVPs are typically sparse (i.e., time variation may occur only episodically and only for some of the coecients). A scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP Vector Autoregressions. In an exercise using arti cial data we demonstrate the accuracy and computational eciency of our methods. In an application involving the term structure of interest rates in the eurozone, we nd our dynamic shrinkage prior to e ectively pick out small amounts of parameter change and our methods to forecast well