Interpretable Proximate Factors for Large Dimensions
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This paper approximates latent statistical factors with sparse and easy-to-interpret proximate factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis, but are usually hard to interpret. By shrinking factor weights, we obtain proximate factors that are easier to interpret. We show that proximate factors consisting of 5-10% of the cross-section observations with the largest absolute loadings are usually sufficient to almost perfectly replicate the population factors, without assuming a sparse structure in loadings. We derive lower bounds for the asymptotic exceedance probability of the generalized correlation between proximate factors and population factors based on extreme value theory, thus providing guidance on how to construct the proximate factors. Simulations and empirical applications to financial single-sorted portfolios and macroeconomic data illustrate that proximate factors approximate latent factors well while being interpretable.
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