# A diagnostic criterion for approximate factor structure

arXiv: https://arxiv.org/abs/1612.04990 · HTML: https://mlsanity.com/paper/1612.04990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2016.

## Built on by (most cited first, 1 of 1)

- [A penalized two-pass regression to predict stock returns with time-varying risk premia](https://mlsanity.com/paper/2208.00972/) (2022)

## Abstract (arXiv)

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.