Efficient selection of hyperparameters in large Bayesian VARs using automatic differentiation |
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Authors: | Joshua C C Chan Liana Jacobi Dan Zhu |
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Institution: | 1. Department of Economics, Purdue University, West Lafayette, Indiana;2. Department of Economics, University of Melbourne, Australia;3. Department of Business Statistics and Econometrics, Monash University, Clayton, Victoria, Australia |
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Abstract: | Large Bayesian vector autoregressions 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 data set, 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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Keywords: | automatic differentiation forecasts marginal likelihood optimal hyperparameters vector autoregression |
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