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

TL;DR

This paper introduces the triple gamma prior, a flexible shrinkage method for variance and variable selection in high-dimensional time-varying parameter models, improving over existing priors in macroeconomic forecasting.

Contribution

The paper proposes the triple gamma prior, unifying several existing shrinkage priors, and demonstrates its effectiveness in TVP models for macroeconomic data.

Findings

Triple gamma prior encompasses Bayesian lasso, double gamma, and Horseshoe priors.

Improves variable selection and variance shrinkage in TVP models.

Shows superior predictive performance in macroeconomic applications.

Abstract

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.