I'm not one for lengthy exposition, so here's a little recollection of the nightmare stairs and a reasonable suggestion from Ezain. 

I've gathered a few ideas regarding his SPI ability. The first is precognition - being able to perceive events before they happen. Now, while we're still weak, he might only be able to glimpse a half-second or less, but as we progress, the length of time can extend well into days or longer, and might show multiple possible outcomes.

The second is simple teleportation - warping himself short distances, and eventually, instantaneously traveling football-field lengths on both X and Y axes in rapid succession.