贝叶斯MIDAS惩罚回归：估计、选择和预测
Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction
摘要：
我们提出了一种新的方法，在高维环境中的混合频率回归，诉诸组套索惩罚和贝叶斯技术的估计和推断。特别是，为了提高模型的预测性能和稀疏恢复能力，我们考虑了一个组Lasso与钉板先验。通过自适应MCMC算法自动调整控制模型收缩的惩罚超参数。我们建立了样本内和样本外预测误差的后验的良好的频率论渐近性质，我们恢复了最佳的后验收缩率，我们显示后验预测密度的最优性。仿真结果表明，所提出的模型在小样本情况下具有良好的选择和预测性能，即使设计矩阵存在互相关。当应用于预测美国GDP时，我们的惩罚回归可以胜过许多强大的竞争对手。结果表明，金融变量可能有一些，虽然非常有限，短期预测的内容。
英文摘要：
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of the model and its sparse recovery ability, we consider a Group Lasso with a spike-and-slab prior. Penalty hyper-parameters governing the model shrinkage are automatically tuned via an adaptive MCMC algorithm. We establish good frequentist asymptotic properties of the posterior of the in-sample and out-of-sample prediction error, we recover the optimal posterior contraction rate, and we show optimality of the posterior predictive density. Simulations show that the proposed models have good selection and forecasting performance in small samples, even when the design matrix presents cross-correlation. When applied to forecasting U.S. GDP, our penalized regressions can outperform many strong competitors. Results suggest that financial variables may have some, although very limited, short-term predictive content.
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