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Title: Triple the gamma: Achieving shrinkage and variable selection in TVP models Authors:  Sylvia Fruehwirth-Schnatter - WU Vienna University of Economics and Business (Austria) [presenting]
Peter Knaus - WU Vienna University of Economics and Business (Austria)
Annalisa Cadonna - WU, Vienna University of Economics and Business (Austria)
Abstract: Time-varying parameter (TVP) models are a popular tool for handling data with smoothly changing parameters. However, in situations with many parameters, the flexibility underlying these models may lead to overfitting models and, as a consequence, to a severe loss of statistical efficiency. This occurs, in particular, if only a few parameters are indeed time-varying, while the remaining ones are constant or even insignificant. As a remedy, hierarchical shrinkage priors have been introduced for TVP models to allow shrinkage both of the initial parameters as well as their variances toward zero. Various approaches to introducing shrinkage priors for TVP models are reviewed. Recently, the (hierarchical) triple Gamma prior has been introduced, which includes other popular shrinkage priors such as the double Gamma prior and the horseshoe prior as a special case. Efficient methods for MCMC inference are also discussed. The close resemblance of the triple Gamma prior with BM is investigated. For illustration, hierarchical shrinkage priors are applied to EU area inflation modelling based on the generalized Phillips curve, to a Cholesky stochastic volatility model, modelling multivariate financial time series of stock returns from the DAX, and to TVP-VAR-SV models, modelling multivariate macroeconomic time series. The results clearly indicate that shrinkage priors reduce the risk of overfitting and increase statistical efficiency in a TVP modelling framework.