Efficient selection of hyperparameters in large Bayesian VARs using automatic differentiation

Author name: 
Chan JCC
Jacobi L
Zhu D

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 data-rich environment.

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