From Rotational to Scalar Invariance: Enhancing Identifiability in Score-Driven Factor Models

This result has no analogue in parameter-driven models, as it exploits the different structure of the score-driven factor dynamics. Consequently, score-driven factor models overcome the issue of rotational invariance that typically affects dynamic factor models, thereby enhancing the economic and financial interpretability of the estimated factors.

Our restrictions are order-invariant and can be generalized to score-driven factor models with dynamic loadings and nonlinear factor models. We test extensively the identification strategy using simulated and real data. The empirical analysis on financial and macroeconomic data reveals a substantial increase of log-likelihood ratios and significantly improved out-of-sample forecast performance when switching from the classical restrictions adopted in the literature to our more flexible specifications.</p>