We disentangle structural breaks in dynamic factor models by establishing a projection based equivalent representation theorem which decomposes any break into a rotational change and orthogonal shift. Our decomposition leads to the natural interpretation of these changes as a change in the factor variance and loadings respectively, which allows us to formulate two separate tests to differentiate between these two cases, unlike the pre-existing literature at large. We derive the asymptotic distributions of the two tests, and demonstrate their good finite sample performance. We apply the tests to the FRED-MD dataset focusing on the Great Moderation and Global Financial Crisis as candidate breaks, and find evidence that the Great Moderation may be better characterised as a break in the factor variance as opposed to a break in the loadings, whereas the Global Financial Crisis is a break in both. Our empirical results highlight how distinguishing between the breaks can nuance the interpretation attributed to them by existing methods.

翻译：我们在动态因子模型中通过建立一个基于投影的等价表示定理来分离结构性断点，该定理将任何断点分解为旋转变化和正交偏移。我们的分解将这些变化自然地解释为因子方差和因子载荷的变动，从而能够制定两个独立的检验来区分这两种情况，这与现有的大部分文献不同。我们推导了这两个检验的渐近分布，并展示了它们良好的有限样本性能。我们将这些检验应用于FRED-MD数据集，重点关注大稳健时期和全球金融危机作为候选断点，发现证据表明，大稳健时期可能更适合被表征为因子方差的断点，而非因子载荷的断点，而全球金融危机则是两者的共同断点。我们的实证结果突显了区分这些断点如何能够为现有方法赋予它们的解释提供细微差别。