  Linear measures such as cross-correlation have been used successfully to
determine time delays from the given processes. Such an analysis often precedes
identifying possible causal relationships between the observed processes. The
present study investigates the impact of a positively correlated driver whose
correlation function decreases monotonically with lag on the delay estimation
in a two-node acyclic network with one and two-delays. It is shown that
cross-correlation analysis of the given processes can result in spurious
identification of multiple delays between the driver and the dependent
processes. Subsequently, delay estimation of increment process as opposed to
the original process under certain implicit constraints is explored.
Short-range and long-range correlated driver processes along with those of
their coarse-grained counterparts are considered.
