The interaction between a fast-speed and a low-speed stream causes large-amplitude Alfvénic fluctuations; consequently, the intermittency and the brief intervals of southward magnetic field associated with Alfvén waves may cause high levels of AE activity, the so-called high-intensity, long-duration, continuous AE activity (HILDCAA). In this article, the 4 h windowed Pearson cross-correlation (4WPCC) between the solar wind velocity and the interplanetary magnetic field (IMF) components is performed in order to confirm that the less strict HILDCAA (HILDCAAs*) events include a larger number of Alfvén waves than the HILDCAA events, once HILDCAAs disregard part of the phenomenon. Actually, a HILDCAA event is entirely contained within a HILDCAA* event. However, the opposite is not necessarily true. This article provides a new insight, since the increase of Alfvén waves results in an increase of auroral electrojet activity; consequently, it can cause HILDCAAs* events. Another important aspect of this article is that the superposed epoch analysis (SEA) results reaffirm that the HILDCAAs* are associated with high-speed solar streams (HSSs), and also the HILDCAAs* present the same physical characteristics of the traditional HILDCAA events.