Computing white stylized facts on comovement

Stylized facts concerning the comovements between two economic variables, as measured by the cross-correlation function of the two filtered variables, reflect a mixture of both the existing cross-correlation between the variables and the autocorrelation structure of each of them. The autocorrelation structure, in turn, crucially depends on the filtering procedure. We propose an alternative method of obtaining stylized facts based on the cross-correlation function of the prewhitened time series, which only depends on the purely stochastic components of the series and the cross effects between them. The relevance of such an approach is tested by revisiting some of the facts reported by Kydland and Prescott [Federal Reserve Bank of Minneapolis, Quarterly Review (1990) 3].