This paper introduces the notion of common noncausal feature and proposes tools for detecting the presence of co-movements in stationary economic and financial time series such as variables with asymmetric cycles or bubbles. For purely noncausal models, i.e., forward looking VARs, we estimate reduced rank regressions in reverse time in order to highlight the potential presence of such noncausal co-movements. For more than one lead or lag, we are able to determine whether the VAR is better represented by purely causal or purely noncausal reduced rank models. Using both sets of lag and lead instruments within a canonical correlation or a GMM framework, additional relationships are discovered between series, both in the Monte Carlo simulations and in empirical illustrations. For mixed causal-noncausal models though, an approximate maximum likelihood estimator assuming non Gaussian disturbances is needed.