Check out Mikkelsen et al. (2015). I've always wanted to try high-dimensional dynamic factor models (DFM's) with time-varying loadings as an approach to network connectedness measurement (e.g., increasing connectedness would correspond to increasing factor loadings...). The problem for me was how to do time-varying parameter DFM's in (ultra) high dimensions. Enter Mikkelsen et al. I also like that it's MLE -- I'm still an MLE fan, per Doz, Giannone and Reichlin. It might be cool and appropriate to endow the time-varying factor loadings with factor structure themselves, which might be a straightforward extension (application?) of Sevanovic (2015). (Stevanovic paper here; supplementary material here.)
Maximum Likelihood Estimation of Time-Varying Loadings in High-Dimensional Factor Models
Jakob Guldbæk Mikkelsen (Aarhus University and CREATES) ; Eric Hillebrand (Aarhus University and CREATES) ; Giovanni Urga (Cass Business School)
In this paper, we develop a maximum likelihood estimator of time-varying loadings in high-dimensional factor models. We specify the loadings to evolve as stationary vector autoregressions (VAR) and show that consistent estimates of the loadings parameters can be obtained by a two-step maximum likelihood estimation procedure. In the first step, principal components are extracted from the data to form factor estimates. In the second step, the parameters of the loadings VARs are estimated as a set of univariate regression models with time-varying coefficients. We document the finite-sample properties of the maximum likelihood estimator through an extensive simulation study and illustrate the empirical relevance of the time-varying loadings structure using a large quarterly dataset for the US economy.