  Complex networked systems can be modeled and represented as graphs, with
nodes representing the agents and the links describing the dynamic coupling
between them. The fundamental objective of network identification for dynamic
systems is to identify causal influence pathways. However, dynamically related
data-streams that originate from different sources are prone to corruption
caused by asynchronous time stamps, packet drops, and noise. In this article,
we show that identifying causal structure using corrupt measurements results in
the inference of spurious links. A necessary and sufficient condition that
delineates the effects of corruption on a set of nodes is obtained. Our theory
applies to nonlinear systems, and systems with feedback loops. Our results are
obtained by the analysis of conditional directed information in dynamic
Bayesian networks. We provide consistency results for the conditional directed
information estimator that we use by showing almost-sure convergence.
