Delay estimation in a two-node acyclic network.

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.