Achieving Shrinkage in a Time-Varying Parameter Model Framework

In the present paper, shrinkage for time-varying parameter (TVP) models is investigated within a Bayesian framework, with the aim to automatically reduce time-varying parameters to static ones, if the model is overfitting. This goal is achieved by formulating appropriate shrinkage priors, in particular, for the process variances, based on the normal-gamma prior (Griffin and Brown, 2010). In this way, we extend previous work based on spike-and-slab priors (Frühwirth-Schnatter and Wagner, 2010) and Bayesian Lasso type priors (Belmonte et al., 2014). We develop an efficient MCMC estimation scheme, exploiting boosting ideas such as ancillarity-sufficiency interweaving (Yu and Meng, 2011). Furthermore, we investigate different priors, including the common inverted gamma prior for the process variances, using a predictive analysis and highlight the advantages of using a Kalman mixture approximation to evaluate one-step ahead predictive densities. Our method is applicable both to TVP models for univariate as well as to multivariate time series. This is exemplified through EU area inflation modelling based on the generalized Phillips curve as well as estimating a time-varying covariance matrix based on a TVP Cholesky stochastic volatility model for a multivariate time series of returns derived from the DAX-30 index. Overall, our findings suggest that the family of shrinkage priors introduced in this paper for TVP models is successful in avoiding overfitting, if potentially time-varying parameters are, indeed, static or even insignificant.