The Consequences of Systematic Sampling on Granger Causality

In applied econometric literature, the causal inferences are often made based on highly temporally aggregated or systematically sampled data. A number of theoretical studies have pointed out that temporal aggregation has distorting effects on causal inference and systematic sampling preserves the direction of causality. This paper examines the issue in detail by plugging in theoretical cross covariances into the limiting values of least squares estimates. The asymptotic distributions of the estimates of systematically sampled process are expressed in terms of the cross covariances of the disaggregated process. An extensive Monte Carlo study is conducted to examine small sample results. Quite contrary to the stationary case where systematic sampling preserves the direction of Granger causality, this paper shows that systematic sampling of integrated series may induce spurious causality, even if, they are used in differenced form. It is observed that in general the most distorting causal inferences are likely at low levels of aggregation where the order of sampling-span just exceeds the actual causal lag. At high levels of aggregation, causal information concentrates in contemporaneous correlations. It is found that if the uni-directional causality runs from a non-stationary series to a stationary or non-stationary series, there is a high likelihood of detecting spurious bi-directional causality