Abstract
Time-varying parameter (TVP) models are very flexible in capturing gradual changes in the effect of explanatory variables on the outcome variable. However, in particular when the number of explanatory variables is large, there is a known risk of overfitting and poor predictive performance, since the effect of some explanatory variables is constant over time. We propose a new 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 dataset and for a series of macroeconomics variables in the Euro Area.
Highlights
Model selection in a high-dimensional setting is a common challenge in statistical and econometric inference
While exploring the full posterior distribution for spike-and-slab priors leads to computational challenges due to the combinatorial complexity of the model space, Bayesian inference based on Markov chain Monte Carlo (MCMC) methods is straightforward for continuous shrinkage priors, exploiting their Gaussian-scale mixture representation (Bitto and Frühwirth-Schnatter 2019; Makalic and Schmidt 2016)
Shrinkage for time-varying parameter (TVP) models was investigated within a Bayesian framework with the goal to automatically reduce time-varying parameters to static ones, if the model is overfitting
Summary
Model selection in a high-dimensional setting is a common challenge in statistical and econometric inference. Once this link has been established, shrinkage priors that are known to perform well in high-dimensional regression problems can be applied to variance selection in state space models, as demonstrated for the Lasso (Belmonte et al 2014) and the normal-gamma (Bitto and Frühwirth-Schnatter 2019; Griffin and Brown 2017) Despite this already existing variety, we introduce a new shrinkage prior for variance selection in sparse state space and TVP models in the present paper called triple gamma prior, as it has a representation involving three gamma distributions. While exploring the full posterior distribution for spike-and-slab priors leads to computational challenges due to the combinatorial complexity of the model space, Bayesian inference based on Markov chain Monte Carlo (MCMC) methods is straightforward for continuous shrinkage priors, exploiting their Gaussian-scale mixture representation (Bitto and Frühwirth-Schnatter 2019; Makalic and Schmidt 2016) An extension of these schemes to the triple gamma prior is fairly straightforward.
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