Common Factors in Conditional Distributions

Dominant properties of various kinds can be defined for distributions including trends, strong seasonality, business cycles, and a persistent component. We say that in the joint distribution of X and Y, conditional on W has a common factor if W is a dominant component, but it does not appear in the copula, only in the conditional marginal distributions for X and Y. An application is discussed involving national income and consumption and a business cycle indicator. The results suggest that the marginals vary with the business cycle but not the copula.