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 the noise terms, thus allowing the update of the time-varying parameter to be potentially nonlinear and robust to outliers. We derive stochastic properties of the 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 to exploit a maximum likelihood estimation on the Stiefel manifolds, which ensure that the identification constraint is satisfied numerically, hence allowing a 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 reveal the empirical usefulness of our factor model for 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 the robust update for the time-varying parameters in the presence of V-shaped recessions, such as the COVID-19 recession.