We develop inferential tools for latent factor analysis in short panels. The pseudo maximum likelihood setting under a large cross-sectional dimension n and a fixed time series dimension T relies on a diagonal TxT covariance matrix of the errors without imposing sphericity nor Gaussianity. We outline the asymptotic distributions of the latent factor and error covariance estimates as well as of an asymptotically uniformly most powerful invariant (AUMPI) test for the number of factors based on the likelihood ratio statistic. We derive the AUMPI characterization from inequalities ensuring the monotone likelihood ratio property for positive definite quadratic forms in normal variables. An empirical application to a large panel of monthly U.S. stock returns separates month after month systematic and idiosyncratic risks in short subperiods of bear vs. bull market based on the selected number of factors. We observe an uptrend in the paths of total and idiosyncratic volatilities while the systematic risk explains a large part of the cross-sectional total variance in bear markets but is not driven by a single factor. Rank tests show that observed factors struggle spanning latent factors with a discrepancy between the dimensions of the two factor spaces decreasing over time.

翻译：我们为短面板中的潜因子分析开发了推断工具。在较大的横截面维度n和固定的时间序列维度T下，伪极大似然设定依赖于误差的TxT对角协方差矩阵，既不要求球形误差假设，也不要求高斯性假设。我们概述了潜因子估计量、误差协方差估计量以及基于似然比统计量的因子数量渐近一致最优势不变检验的渐近分布。该渐近一致最优势不变特性的推导源于确保正态变量正定二次型具有单调似然比性质的不等式。通过对美国月度股票收益大面板数据的实证应用，我们基于所选因子数量，在熊市与牛市短期子区间内逐月分离了系统性风险与异质性风险。我们观察到总波动率与异质性波动率路径呈上升趋势，同时系统性风险在熊市中解释了横截面总方差的很大部分，但并非由单一因子驱动。秩检验表明，观测因子难以张成潜因子，且两个因子空间维度间的差异随时间逐渐减小。