Is it a short-memory, long-memory, or permanently Granger-causation influence?

Exploring the Granger-causation relationship is an important and interesting topic in the field of econometrics. In the traditional model we usually apply the short-memory style to exhibit the relationship, but in practice there could be other different influence patterns. Besides the short-memory relationship, Chen (2006) demonstrates a long-memory relationship, in which a useful approach is provided for estimation where the time series are not necessarily fractionally co-integrated. In that paper two different relationships (short-memory and long-memory relationship) are regarded whereby the influence flow is decayed by geometric, or cutting off, or harmonic sequences. However, it limits the model to the stationary relationship. This paper extends the influence flow to a non-stationary relationship where the limitation is on -0.5≤d≤1.0 and it can be used to detect whether the influence decays off (-0.5≤d≤0.5) or is permanent (0.5≤d≤1.0).