Inference in Sparsity-Induced Weak Factor Models
Inference in Sparsity-Induced Weak Factor Models
复制标题
DOI：
10.1080/07350015.2021.2003203
复制
发表时间：
2020-03
影响因子：
3
通讯作者：
Yoshimasa Uematsu;Takashi Yamagata
中科院分区：
文献类型：
--
作者：
Yoshimasa Uematsu;Takashi Yamagata
摘要在这篇文章中，我们考虑了高维近似因子模型的统计推断。我们假设一个弱因子结构，其中因子加载矩阵可以是稀疏的，并且信号特征值的发散可能比横截面维度N更慢。我们提出了一种新的推理过程，以决定是否每个组件的因素负载为零或不，并证明这控制的错误发现率（FDR）低于预先指定的水平，而权力趋于统一。这个“因子选择”过程主要是基于稀疏正交因子回归（SOFAR）估计量的去偏版本，但也适用于主成分（PC）估计量。在因子选择之后，提出了再稀疏化的SOFAR和稀疏化的PC估计，并证明了它们的相合性。有限的样本证据支持理论结果。我们将我们的方法应用于FRED-MD数据集的宏观经济变量和月度公司层面的超额收益，构成标准普尔500指数。结果给出了非常有力的统计证据稀疏的因素负荷下的识别限制，并表现出明确的关联因素和类别的变量。此外，我们的方法揭示了一个非常弱的，但统计上显着的因素，在残差的法玛-法国五因素回归。
Abstract In this article, we consider statistical inference for high-dimensional approximate factor models. We posit a weak factor structure, in which the factor loading matrix can be sparse and the signal eigenvalues may diverge more slowly than the cross-sectional dimension, N. We propose a novel inferential procedure to decide whether each component of the factor loadings is zero or not, and prove that this controls the false discovery rate (FDR) below a preassigned level, while the power tends to unity. This “factor selection” procedure is primarily based on a debiased version of the sparse orthogonal factor regression (SOFAR) estimator; but is also applicable to the principal component (PC) estimator. After the factor selection, the resparsified SOFAR and sparsified PC estimators are proposed and their consistency is established. Finite sample evidence supports the theoretical results. We apply our method to the FRED-MD dataset of macroeconomic variables and the monthly firm-level excess returns which constitute the S&P 500 index. The results give very strong statistical evidence of sparse factor loadings under the identification restrictions and exhibit clear associations of factors and categories of the variables. Furthermore, our method uncovers a very weak but statistically significant factor in the residuals of Fama-French five factor regression.