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.

中文翻译：

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使用自动微分有效选择大型贝叶斯 VAR 中的超参数

具有自然共轭先验的大贝叶斯向量自回归现在通常用于预测和结构分析。已经表明，以数据驱动的方式选择先验超参数通常可以显着提高预测性能。我们提出了一种基于自动微分的计算效率高的方法来获得最佳超参数，这是一种计算导数的有效方法。使用大型美国数据集，我们表明使用最佳超参数值可以显着提高预测性能。此外，所提出的方法比传统的网格搜索方法快得多，适用于高维优化问题。