Does Systematic Sampling Preserve Granger Causality with an Application to High Frequency Financial Data?

Abstract

In applied econometric literature, the causal inferences are often made based on 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 of stationary variables 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 in a VAR framework. 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, this paper shows that systematic sampling of integrated series may induce spurious causality. In particular, systematic sampling induces spurious bi-directional Granger causality among the variables if the uni-directional causality runs from a non-stationary series to either a stationary or a non-stationary series. On the other hand, systematic sampling preserves the uni-directional causality among the variables if the uni-directional causality runs from a stationary series to either a stationary or a non-stationary series. It is observed that in general the most distorting causal inferences are likely at low levels of sampling intervals where the order of sampling-span just exceeds the actual causal lag. At high levels of systematic sampling, causal information concentrates in contemporaneous correlations. An empirical exercise illustrates the relative usefulness of the results further.