Latent Factor Analysis in Short Panels
为短面板数据开发了潜在因子分析的推断工具，包括因子和误差协方差的渐近分布以及基于似然比统计量的因子个数检验，并应用于美国股票月度收益数据以区分系统性和异质性风险。
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 T x T covariance matrix of the errors without imposing sphericity or 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 based on the likelihood ratio statistic for tests of the number of factors. 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 date after date systematic and idiosyncratic risks in short subperiods of bear vs. bull market based on the selected number of factors. We observe an uptrend in idiosyncratic volatility 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 reveal that observed factors struggle spanning latent factors with a discrepancy between the dimension of the two factor spaces decreasing over time.