Temporal aggregation and spurious causation in time series

The issue of temporal aggregation in time series has been discussed extensively in the last decades. There is a general consensus (see Breitung and Swanson, 2002) on the spurious effects produced by aggregation. In particular, one may observe that two time series originally uncorrelated after aggregation can result in non-zero correlation. When more time series are jointly considered, it becomes rather complicated to distinguish the effect of aggregation. In order to detect the presence of spurious effects due to temporal aggregation we propose a class of tests for instantaneous noncausality between groups of variables in a VAR(p) setting. According to the definition of Granger (1969), instantaneous causality means that the knowledge of the current value of a series xt helps in predicting the current value of a series yt. The application of the class of tests proposed is illustrated by some examples with macroeconomic data. In particular, using the small macroeconometric model for the U.S. monetary system introduced by Christiano, Eichenbaum and Evans (1996) we find that the real variables react to monetary policy shocks with a delay which can be quantified between one and three months, which is consistent with Christiano, Eichenbaum and Evans (1996)’ results.