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Time-varying parameter (TVP) regression models can involve a huge number ofcoefficients. Careful prior elicitation is required to yield sensible posteriorand predictive inferences. In addition, the computational demands of MarkovChain Monte Carlo (MCMC) methods mean their use is limited to the case wherethe number of predictors is not too large. In light of these two concerns, thispaper proposes a new dynamic shrinkage prior which reflects the empiricalregularity that TVPs are typically sparse (i.e. time variation may occur onlyepisodically and only for some of the coefficients). A scalable MCMC algorithmis developed which is capable of handling very high dimensional TVP regressionsor TVP Vector Autoregressions. In an exercise using artificial data wedemonstrate the accuracy and computational efficiency of our methods. In anapplication involving the term structure of interest rates in the eurozone, wefind our dynamic shrinkage prior to effectively pick out small amounts ofparameter change and our methods to forecast well.

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