It's pretty obvious that Purgatorio has first person narration. Dante says “I” all the time. In fact, it’s a very “me, me!” kind of text. Here, perhaps even more than in the Inferno, we’re hit over the head with the idea that this journey is all happening for Dante’s education. However, the author-Dante and character-Dante division (identified in Inferno) still applies. Author-Dante influences the text by providing characters with knowledge they shouldn’t possess – yet. In other words, author-Dante has already lived through all these events and is therefore able to “foresee” events that haven’t happened in character-Dante’s time. This is why he’s able to give the penitents “foresight,” which he attributes to their non-mortal state.
All these confusing time issues aside, there is one interesting passage in which Dante is not explicitly the narrator. Canto XIV begins with a conversation between Guido del Duca and Rineri da Calboli. It looks for a moment as if the point of view has shifted to third person omniscient because Dante is nowhere to be seen. However, after several lines of dialogue, we find that Dante-character is watching them. That is the only reason why we don’t have a quick blip of third person omniscient in here.