高维隐含因子与定价误差的协同估计

高维隐含因子模型在高维金融数据分析中有广泛的应用。近年来大量金融实证研究指出主流的隐含因子估计方法主成分分析(PCA)法估计的因子可以较好地解释资产的风险，但不足之处在于对解释横截面预期回报方面差强人意。本项目将研究高维隐含因子模型的有效估计。我们提出将定价误差以及特质收益各异性这些重要的特质收益矩特征纳入模型估计的统计方法。由该方法恢复的模型将能同时解释高维资产收益的风险和预期回报。在理论方面，我们将建立该方法在高维环境下因子和定价误差估计的统计性质。本项目的研究成果不仅会弥补利用特质收益均值与协方差矩阵的矩信息在高维隐含因子模型估计方法及理论研究方面的缺失，同时在金融应用中，为资产定价模型的构建与检验、高维投资组合优化、风险管理等提供有效的统计工具。

High-dimensional latent factor model is widely used in the study of financial big data. In the finance literature, it has been documented that the latent factors estimated from Principal Component Analysis (PCA) works well in explaining the risk but fails in explaining the cross-sectional expected returns. In this project, we will develop statistical framework to efficiently recover the latent factor models which can explain both the risk and expected returns of a large number of assets. The proposed estimator will take account of the pricing error and heteroskedasticity in idiosyncratic returns in the model estimation. We will establish the consistency properties of the proposed estimators of the factors models including the pricing error under the high-dimensional setting. The methodology we develop in this project will contribute to the statistics literature in high-dimensional latent factor model estimation and provide statistical tools to the financial applications such as asset pricing study, high-dimensional portfolio optimization and risk management.