On the Ordering of Dynamic Principal Components and the Implications for Portfolio Analysis

When principal component analysis is used on a rolling or conditional setting, ordering and incoherence issues may emerge. We provide empirical evidence supporting this claim and introduce an algorithm that allows dynamic reordering of the principal components (PCs). We provide additional results that shed light on the consequences of incoherence when analyzing the link between PCs and macroeconomic risk factors, with a focus on the COVID-19 pandemic period. When PCs are optimally reordered, the roles of factors emerge more clearly, with relevant implications for risk management.