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Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models

Department of Finance, Accounting and Statistics, WU Vienna University of Economics and Business, 1020 Vienna, Austria
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Econometrics 2020, 8(2), 20; https://doi.org/10.3390/econometrics8020020
Received: 9 December 2019 / Revised: 6 April 2020 / Accepted: 29 April 2020 / Published: 20 May 2020
(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)
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. View Full-Text
Keywords: Bayesian model averaging; horseshoe prior; lasso prior; sparsity; stochastic volatility; triple gamma prior; VAR models Bayesian model averaging; horseshoe prior; lasso prior; sparsity; stochastic volatility; triple gamma prior; VAR models
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Cadonna, A.; Frühwirth-Schnatter, S.; Knaus, P. Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models. Econometrics 2020, 8, 20.

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