标题： 从旋转不变性到标量不变性：增强评分驱动因子模型的可识别性 显示英文标题

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

摘要： 我们证明，对于一类包括常用条件Fisher信息的逆平方根在内的缩放矩阵，得分驱动因子模型在非常轻微的限制下是可识别的，最多相差一个乘法标量常数。 这一结果在参数驱动模型中没有对应情况，因为它利用了得分驱动因子动态的不同结构。 因此，与仅能通过正交变换识别的参数驱动因子模型相比，得分驱动模型在经济可解释性方面具有明显优势。 我们的限制条件与顺序无关，并可以推广到具有动态载荷和非线性因子模型的得分驱动因子模型。 我们使用模拟数据和实际数据对识别策略进行了广泛测试。 对金融和宏观经济数据的实证分析显示，当从文献中采用的经典限制转向我们更灵活的规范时，对数似然比显著增加，样本外预测性能显著提高。 显示英文摘要

摘要： 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.