The film is a traditional chronological narrative—no flashbacks or flash-forwards, no postmodern jumping around or playing with concepts of time and space.
Technically, we're bending the rules by calling it a first-person narrative. A real first-person story would use things like voice-over and constant POV shots to get us into the main character's head. Hitchcock doesn't quite do that—but, frankly speaking, he doesn't need to. We spend every second by Jeff's side, seeing what he's seeing and stuck in the apartment just like he is. Except for one brief scene at the very end of the movie, the camera never leaves his wheelchair.
That probably qualifies it for first-person status, despite the fact that it doesn't quite fit the strict definition. The only real difference is one of technique—Hitchcock does it all visually.