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Unlike previous studies, the methodology of this paper allows FIML estimation of the restricted VAR\/VECM and therefore the extraction of the unobserved codependent cyclical components via a Beveridge\u2010Nelson decomposition. It is further shown that the number and order of cofeature combinations that yield the scalar component models associated with codependence is limited by the dimension of a finite\u2010order VAR system. Monte Carlo simulations indicate that LR tests based on FIML estimates have higher power than alternative GMM and canonical correlations tests, while maintaining good size properties. An empirical application investigates the presence of codependence in UK consumption data. 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