Codependent cycles

This paper extends the work of Engle and Kozicki (1993) to test for co-movement in multiple time series when their cycles are not exactly synchronized. We call these codependent cycles and show that testing and estimation in this case will be a Generalized Method of Moments test and estimation procedure. We also show that the Tiao and Tsay (1985) proposed test for scalar components models of order (0,q) can be seen as a test for codependent cycles based on a consistent, but sub-optimal, estimate of the cofeature vector. We assess the small sample performance of the proposed tests through a series of simulations. Finally we apply this test to investigate comovement between durable and non-durable consumption expenditures.