Disentangling Structural Breaks in High Dimensional Factor Models

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.