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.