Observable versus Latent Factors
Journal of the American Statistical Association · Tue
DOI: 10.1080/01621459.2026.2701436
Abstract
We test for temporal stability in local linear projection coefficients of observable factors on latent ones embedded in a high-dimensional vector obeying a linear factor model. The proposed test explores the fact that, under the null hypothesis, residuals from global linear projections of observable factors on latent ones, computed over a fixed time interval via Principal Component Analysis (PCA), should also be locally uncorrelated with the PCA factors. The test is fully nonparametric. Its asymptotic behavior is derived under a joint infill and large cross-section asymptotic setup. The test can be used to decide whether and over what horizon observable factors can be linearly spanned by latent ones. In an empirical application, we show that a linear relation between the market volatility factor and the latent systematic risk factors embedded in the cross-section of stock returns exists only over short periods of length of one trading day. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
Keywords
High-frequency data, Latent factor model, Nonparametric test, PCA
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