Estimation of factors using higher-order multi-cumulants in weak factor models

When factors are weak, covariance-based factor analysis methods tend to exhibit poor performance. To address this issue in the case of non-Gaussian data, we propose a new method called Higher-order multi-cumulant Factor Analysis (HFA). HFA estimates factors and factor loadings via the eigenvalue decomposition of the product of a higher-order multi-cumulant matrix and its transpose. We derive the asymptotic properties of HFA under a weak factor model where non-Gaussianity originates solely from the latent factors, while idiosyncratic errors remain Gaussian. Simulation studies demonstrate that HFA significantly improves both factor selection and estimation when factors are weak and non-Gaussian, compared with traditional methods. Applied to the FRED-MD dataset, HFA identifies factors that improve out-of-sample forecasting performance for the S&P 500 monthly equity premium.