Temporal Aggregation and Causality in Multiple Time

Large aggregation interval asymptotics are used to investigate the relation between Granger causality in disaggregated vector autoregressions (VARs) and associated contemporaneous correlation among innovations of the aggregated system. Our approach allows us to better understand the informational content in non-diagonal error covariance matrices, which play an important role in structural VAR analysis, for example. From a theoretical perspective, we outline various conditions under which the informational content of error covariance matrices yields insight into the causal structure of the VAR. Tis allows us, for example, to summarize the types of empirical questions which can be answered by evaluating the correlation structure of error covariance matrices in aggregated VARs. Monte Carlo results suggest that our asymptotic ̄ndings are applicable even when the aggregation interval is small, as long as the time series are not characterized by high levels of persistence. JEL Classi ̄cation: C32, C43, C51.