Disentangling Structural Breaks in High Dimensional Factor Models

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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.

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