Working Paper

Factor Models with Local Factors—Determining the Number of Relevant Factors

Abstract: We extend the theory on factor models by incorporating “local” factors into the model. Local factors affect only an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. We de-rive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. We then introduce a new class of estimators to determine the number of those relevant factors. Un-like existing estimators, our estimators use not only the eigenvalues of the covariance matrix, but also its eigenvectors. We find that incorporating partial sums of the eigenvectors into our estimators leads to significant gains in performance in simulations.

Keywords: high-dimensional data; factor models; weak factors; local factors; sparsity;

JEL Classification: C38; C52; C55;

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Bibliographic Information

Provider: Federal Reserve Bank of Philadelphia

Part of Series: Working Papers

Publication Date: 2021-04-15

Number: 21-15

Note: Supersedes Working Paper 19-23 – A Generalized Factor Model with Local Factors