Using different methods, most of the research articles on epilepsy analyze the structures of different neurological states (interictal, pre-ictal, ictal and post-ictal) to determine their distinguishing properties. On the other hand, some studies investigate the causal relationship between interictal state, pre-ictal and ictal state, especially in order to predict the seizures from the interictal EEG activities. This type of usage of the interictal data mathematically needs the imposition of some constraints which in turn may prevent researchers to extract more useful information hidden in the interictal EEG data. In the present study: firstly, we explore the non-stationary behavior of focal interictal epileptiform series within very short time intervals: secondly, for such intervals we analyzed the revealed short-run and long-run interaction mechanisms of neuronal ensembles. Here we find: first, that short interictal series contains unit root and can be represented as autoregressive integrated moving average (ARIMA) process: second, between the interictal EEG signals there exists bidirectional causality (anthogonist effects) in the long-run. Therefore, in the long-run neither of the synchronized neuronal assemblies are positively affected (increasing amplitudes) from this relationship. Moreover, the long-run mechanism originated by co-movement (cointegration) of the interictal series reveals why there should not be a causal link from the interictal state to ictal state. (C) 2009 Elsevier Inc. All rights reserved.