An Extended Score-Driven Dynamic Factor Model: Constructing Composite Indices in Turbulent Times

We propose an extended score-driven (ESD) dynamic factor model (DFM) that can accommodate non-Gaussian innovations, nonlinear factor dynamics, and time-varying volatility. The main novelty of our model is a state equation that includes both lagged and contemporaneous scores, implying that factors are not predetermined. We show that this novel model nests both the classic (parameter-driven) state-space DFM as well as the more recent score-driven DFM, bridging the gap between these two model classes. Empirically, our ESD-DFM proves useful for working with (post-)COVID-19-era observations, which have posed substantial challenges for macroeconomic modeling. For instance, while the Federal Reserve Bank of Philadelphia suspended publication of its leading index due to pandemic-related anomalies, our model remains robust to such extreme observations and enables reliable computation of the index. We further apply the ESD-DFM to The Conference Board’s (TCB's) Coincident and Leading Economic Indices (CEI and LEI). When indices are constructed from the estimated factors, the unprecedented divergence between TCB's CEI and LEI observed during the post-pandemic period disappears: although the reconstructed LEI declines in 2022, it resumes an upward trajectory from the second half of 2023 through the end of 2025.