A diagnostic criterion for approximate factor structure

Patrick Gagliardini (), Elisa Ossola () and Olivier Scaillet

Abstract: We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly cross-sectionally correlated or share at least one unobservable common factor. It only requires computing the largest eigenvalue of the empirical cross-sectional covariance matrix of the residuals of a large unbalanced panel. A general version of this criterion allows us to determine the number of omitted common factors. The panel data model accommodates both time-invariant and time-varying factor structures. The theory applies to random coefficient panel models with interactive fixed effects under large cross-section and time-series dimensions. The empirical analysis runs on monthly and quarterly returns for about ten thousand US stocks from January 1968 to December 2011 for several time-invariant and time-varying specifications. For monthly returns, we can choose either among time-invariant specifications with at least four financial factors, or a scaled three-factor specification. For quarterly returns, we cannot select macroeconomic models without the market factor.

Date: 2016-12, Revised 2017-08
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: A diagnostic criterion for approximate factor structure (2019)
Working Paper: A Diagnostic Criterion for Approximate Factor Structure (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1612.04990

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