The Dynamic, the Static, and the Weak: Factor models and the analysis of high-dimensional time series

Several fundamental and closely interconnected issues related to factor models are reviewed and discussed: dynamic versus static loadings, rate-strong versus rate-weak factors, the concept of weakly common component recently introduced by Gersing et al. (2023), the irrelevance of cross-sectional ordering and the assumption of cross-sectional exchangeability, the impact of undetected strong factors, and the problem of combining common and idiosyncratic forecasts. Conclusions all point to the advantages of the General Dynamic Factor Model approach of Forni et al. (2000) over the widely used Static Approximate Factor Model introduced by Chamberlain and Rothschild (1983).