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Title: Horseshoe prior Bayesian quantile regression Authors:  Tibor Szendrei - Heriot-Watt University (United Kingdom)
David Kohns - Heriot-Watt University (United Kingdom) [presenting]
Abstract: The Horseshoe Prior is extended to the Bayesian Quantile Regression (HS-BQR), a fast sampling algorithm is provided that speeds up computation significantly in high dimensions. The performance of the HS-BQR is tested on large scale Monte Carlo simulations and a high dimensional Growth-at-Risk (GaR) forecasting exercise for the U.S. The Monte Carlo design considers several sparsity structures (sparse, dense, block) and error structures (i.i.d. errors and heteroskedastic errors). Compared to alternative shrinkage priors, the proposed HS-BQR yields at worst similar, or better performance considered when evaluated using coefficient bias and forecast error. We find that the HS-BQR is particularly potent in sparse designs and when estimating extreme quantiles. The simulations also highlight that in order to identify quantile specific location and scale effects for individual regressors in dense DGPs, a lot of data are necessary. In the GaR application, we forecast tail risks as well as complete forecast densities using the McCracken database. Quantile specific and density calibration scoring functions show that the HS-BQR provides the best performance, especially at short and medium run horizons. The ability to produce well calibrated density forecasts and accurate downside risk measures in the face of large data contexts makes the HS-BQR a promising tool for nowcasting applications and recession modelling in the face of the Covid-19 pandemic.