From rotational to scalar invariance: Enhancing identifiability in score-driven factor models

TL;DR

This paper demonstrates that score-driven factor models are identifiable up to a scalar constant under mild conditions, offering better interpretability and improved forecasting performance compared to parameter-driven models.

Contribution

It introduces a novel identification approach for score-driven factor models that generalizes to dynamic loadings and nonlinear models, enhancing interpretability and empirical performance.

Findings

Score-driven models are identifiable up to a scalar constant.

Empirical results show improved log-likelihood and forecast accuracy.

The proposed restrictions are order-invariant and broadly applicable.

Abstract

We show that, for a certain class of scaling matrices including the commonly used inverse square-root of the conditional Fisher Information, score-driven factor models are identifiable up to a multiplicative scalar constant under very mild restrictions. This result has no analogue in parameter-driven models, as it exploits the different structure of the score-driven factor dynamics. Consequently, score-driven models offer a clear advantage in terms of economic interpretability compared to parameter-driven factor models, which are identifiable only up to orthogonal transformations. Our restrictions are order-invariant and can be generalized to scoredriven 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.