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

Simon Freyaldenhoven

No 21-15, Working Papers from Federal Reserve Bank of Philadelphia

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 (search for similar items in EconPapers)
JEL-codes: C38 C52 C55 (search for similar items in EconPapers)
Pages: 39
Date: 2021-04-15
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Note: Supersedes Working Paper 19-23 – A Generalized Factor Model with Local Factors
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Citations: View citations in EconPapers (4)

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Journal Article: Factor models with local factors — Determining the number of relevant factors (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:fip:fedpwp:90903

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DOI: 10.21799/frbp.wp.2021.15

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