A measure of comovement for economic variables: Theory and empirics

This paper proposes a measure of dynamic comovement between (possibly many) time series and names it cohesion. The measure is defined in the frequency domain and is appropriate for processes that are costationary, possibly af ter suitable transformations. In the bivariate case, the measure reduces to dynamic correlation and is related, but not equal, to the well known quant ities of coherence and coherency. Dynamic correlation on a frequency band e quals (static) correlation of bandpass-filtered series. Moreover, long-run correlation and cohesion relate in a simple way to co-integration. Cohesion is useful to study problems of business-cycle synchronization, to investig ate short-run and long-run dynamic properties of multiple time series, and to identify dynamic clusters. We use state income data for the United State s and GDP data far European nations to provide an empirical illustration th at is focused on the geographical aspects of business-cycle fluctuations.