Eigenvalue Tests for the Number of Latent Factors in Short Panels
研究了时间维度小、横截面维度大的因子模型中潜在因子数量的检验方法，基于资产收益协方差矩阵的特征值，并应用于美国股票数据，发现市场涨跌期因子数量差异在统计上不明确。
Abstract This article studies new tests for the number of latent factors in a large cross-sectional factor model with small time dimension. These tests are based on the eigenvalues of variance–covariance matrices of (possibly weighted) asset returns and rely on either an assumption of spherical errors, or instrumental variables for factor betas. We establish the asymptotic distributional results using expansion theorems based on perturbation theory for symmetric matrices. Our framework accommodates semi-strong factors in the systematic components. We propose a novel statistical test for weak factors against strong or semi-strong factors. We provide an empirical application to U.S. equity data. Evidence for a different number of latent factors according to market downturns and market upturns is statistically ambiguous in the considered subperiods. In particular, our results contradict the common wisdom of a single-factor model in bear markets.