In this paper, we propose and evaluate a shrinkage based methodology that is designed to improve the accuracy of volatility forecasts. Our approach is based on a two-step procedure for extracting latent common volatility factors from a large dimensional and high-frequency dataset. In the first step, we apply either least absolute shrinkage operator (LASSO) or the elastic net (EN) shrinkage on estimated integrated volatilities, in order to select a subset of assets that are informative about the target asset. In the second step, we utilize (sparse) principal component analysis on the selected assets, in order to estimate latent return factors, which are in turn used to construct latent volatility factors. Our two-step method is found to yield more accurate volatility predictions than a variety of alternative models based on approaches such as direct application of (S)PCA and direct application of LASSO or EN shrinkage, when comparing out-of-sample $R^2$s and mean absolute forecasting errors, and when implementing predictive accuracy tests. Additionally model confidence sets are found to contain models solely based on our two-step approach. These forecasting gains are found to be robust to the use of original or log-scale realized volatility models, different data sampling frequencies, and different forecasting sub-periods.

在本文中，我们提出并评估了基于收缩的方法，该方法旨在提高波动率预测的准确性。我们的方法基于两步过程，可从大型多维数据集和高频数据集中提取潜在的常见波动性因子。在第一步中，我们对估计的综合波动率应用最小绝对收缩算子（LASSO）或弹性净收缩（EN）收缩，以选择可提供有关目标资产信息的资产子集。在第二步中，我们对选定的资产进行（稀疏）主成分分析，以估计潜在的回报因子，然后将其用于构建潜在的波动性因子。样本外 ${\mathrm{[R}}^{\mathrm{2个}}$s和平均绝对预测误差，以及实施预测准确性测试时。另外，发现模型置信集仅包含基于我们的两步法的模型。发现这些预测增益对于使用原始或对数标度实现的波动率模型，不同的数据采样频率以及不同的预测子周期具有鲁棒性。