  We consider the effect of temporal aggregation on instantaneous
(non-temporal) causal discovery in general setting. This is motivated by the
observation that the true causal time lag is often considerably shorter than
the observational interval. This discrepancy leads to high aggregation, causing
time-delay causality to vanish and instantaneous dependence to manifest.
Although we expect such instantaneous dependence has consistency with the true
causal relation in certain sense to make the discovery results meaningful, it
remains unclear what type of consistency we need and when will such consistency
be satisfied. We proposed functional consistency and conditional independence
consistency in formal way correspond functional causal model-based methods and
conditional independence-based methods respectively and provide the conditions
under which these consistencies will hold. We show theoretically and
experimentally that causal discovery results may be seriously distorted by
aggregation especially in complete nonlinear case and we also find causal
relationship still recoverable from aggregated data if we have partial
linearity or appropriate prior. Our findings suggest community should take a
cautious and meticulous approach when interpreting causal discovery results
from such data and show why and when aggregation will distort the performance
of causal discovery methods.
