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.