Triple the gamma -- A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models

Time-varying parameter (TVP) models are very flexible in capturing gradual changes in the effect of a predictor on the outcome variable. However, in particular when the number of predictors is large, there is a known risk of overfitting and poor predictive performance, since the effect of some predictors is constant over time. We propose a prior for variance shrinkage in TVP models, called triple gamma. The triple gamma prior encompasses a number of priors that have been suggested previously, such as the Bayesian lasso, the double gamma prior and the Horseshoe prior. We present the desirable properties of such a prior and its relationship to Bayesian Model Averaging for variance selection. The features of the triple gamma prior are then illustrated in the context of time varying parameter vector autoregressive models, both for simulated datasets and for a series of macroeconomics variables in the Euro Area.