Detecting Co-Movements in Noncausal Time Series

This paper introduces the notion of common noncausal features and proposes tools for detecting the presence of co-movements in economic and financial time series subject to phenomena such as asymmetric cycles and speculative bubbles. For purely causal or noncausal vector autoregressive models with more than one lag, the presence of a reduced rank structure allows to identify causal from noncausal systems using the usual Gaussian likelihood framework. This result cannot be extended to mixed causal-noncausal models, and an approximate maximum likelihood estimator assuming non-Gaussian disturbances is needed for this case. We find common bubbles in both commodity prices and price indicators.