We propose a model to forecast large realized covariance matrices of returns, applying it to the constituents of the S&P 500 daily. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value, and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive models with the least absolute shrinkage and selection operator. Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of minimum variance portfolios.

中文翻译：

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预测大型已实现的协方差矩阵：因子模型和收缩的好处

我们提出了一个模型来预测回报的大型已实现协方差矩阵，并将其每天应用于标准普尔 500 指数的成分股。为了解决维数灾难，我们使用标准的公司层面因素（例如，规模、价值和盈利能力）分解回报协方差矩阵，并在残差协方差矩阵中使用部门限制。然后使用具有最小绝对收缩和选择算子的向量异构自回归模型来估计该受限模型。我们的方法提高了相对于标准基准的预测精度，并可以更好地估计最小方差投资组合。