Are They Swinging Together? A measure of linear comovement with an application

This is a revised version of chapter II in my forthcoming thesis at Massachusetts Institute of Technology. A frequency band specific measure of the degree of linear comovement is defined. The distribution of the measure is simulated using Monte Carlo methods. The sensitivity of the distributions to the characteristics of the underlying processes is substantially reduced if low frequencies are excluded from the analysis. It is argued that "business cycle facts" established using filters that include low frequencies, for example the Hodrick-Prescott filter, may be dominated by the behavior at low frequencies. Explicit treatment of different frequency bands may then be preferable. The measure of linear comovement is applied to Swedish and foreign macro time series spanning the period 1861 to 1988. A substantial degree of comovement between Swedish consumption related variables and foreign GDP is found while Swedish GDP and manufacturing production is clearly less covariant with foreign GDP.