Efficient Selection of Hyperparameters in Large Bayesian VARs Using Automatic Differentiation

Large Bayesian VARs with the natural conjugate prior are now routinely used for
forecasting and structural analysis. It has been shown that selecting the prior
hyperparameters in a data-driven manner can often substantially improve forecast
performance. We propose a computationally efficient method to obtain the optimal
hyperparameters based on Automatic Differentiation, which is an efficient way to
compute derivatives. Using a large US dataset, we show that using the optimal
hyperparameter values leads to substantially better forecast performance. Moreover, the
proposed method is much faster than the conventional grid-search approach, and is
applicable in high-dimensional optimization problems. The new method thus provides a
practical and systematic way to develop better shrinkage priors for forecasting in a datarich
environment.