From rotational to scalar invariance: Enhancing identifiability in score-driven factor models
研究得分驱动因子模型的可识别性，证明在弱限制下可识别至标量常数，克服旋转不变性问题，提升因子解释性。模拟和金融宏观经济数据验证显示预测表现提升，适合关注动态因子模型的学者。
We show that, for a certain class of scaling matrices including the 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 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.