Temporal aggregation and causality in multiple time series models

In this paper we characterize what has sometimes been referred to in the literature as instantaneous causality, by examining the consequences of temporal aggregation in (possibly) Granger causal systems of variables. Our approach is to compare the concept of contemporaneous correlation due to Swanson and Granger (1997) with that of Granger causality. Using asymptotic theory based on large aggregation intervals we derive conditions for a correspondence between both concepts. These results allow us to differentiate between spurious contemporaneous correlation arising because of aggregation, and true Granger causality. Monte Carlo experiments indicate that the asymptotic results provide a reliable guidance for finite samples and finite aggregation intervals.