An order-invariant score-driven dynamic factor model

This paper introduces a novel score-driven dynamic factor model designed for filtering cross-sectional co-movements in panels of time series. The model is formulated using elliptical distribution for noise terms, allowing the update of the time-varying parameter to be potentially nonlinear and robust to outliers. We derive stochastic properties of time series generated by the model, such as stationarity and ergodicity, and establish the invertibility of the filter. We prove that the identification of the factors and loadings is achieved by incorporating an orthogonality constraint on the loadings, which is invariant to the order of the series in the panel. Given the nonlinearity of the constraint, we propose exploiting a maximum likelihood estimation on Stiefel manifolds. This approach ensures that the identification constraint is satisfied numerically, enabling joint estimation of the static and time-varying parameters. Furthermore, the asymptotic properties of the constrained estimator are derived. In a series of Monte Carlo experiments, we find evidence of appropriate finite sample properties of the estimator and resulting score filter for the time-varying parameters. We demonstrate the empirical usefulness of our factor model in constructing indices of economic activity from a set of macroeconomic and financial variables during the period 1981–2022. An empirical application highlights the importance of robustness, particularly in the presence of V-shaped recessions, such as the COVID-19 recession.