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Time-varying parameter (TVP) models are very flexible in capturing gradualchanges in the effect of a predictor on the outcome variable. However, inparticular when the number of predictors is large, there is a known risk ofoverfitting and poor predictive performance, since the effect of somepredictors is constant over time. We propose a prior for variance shrinkage inTVP models, called triple gamma. The triple gamma prior encompasses a number ofpriors that have been suggested previously, such as the Bayesian lasso, thedouble gamma prior and the Horseshoe prior. We present the desirable propertiesof such a prior and its relationship to Bayesian Model Averaging for varianceselection. The features of the triple gamma prior are then illustrated in thecontext of time varying parameter vector autoregressive models, both forsimulated datasets and for a series of macroeconomics variables in the EuroArea.

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