Here are links to two Twitter conversations where he mentions the time (I was able to find the second one because I had recalled that he made a joke regarding the Hinterlands). Part 1 & Part 2.
I honestly wish he hadn't said anything because then you get threads like this speculating on whether he "pulled the number out of his ass," people trying to refute it with various in-game examples, or others just stating how long it felt to them (I'll be guilty of these latter two).
Like others, I feel that the time scope is not represented well in the game at all. The area DAI takes place in is very large. As far as I can recall, we've only gotten two distance measurements throughout the entire DA series, and both are in DAO. When you ask Alistair about the other Wardens at Weisshaupt he says "that's a thousand miles from here," but I don't know whether that is 'as the crow flies' or the standard travel over land and roads. Also, if you speak to Dagna again without having been to the Circle, she says that it takes nine days to get from Orzammar to the Circle (my memory is foggy here, it's been quite a while since I played DAO).
It takes significant time (up to a month!) to travel to and from (up to two moths both ways!) each of the locations we visit, in addition to the actual time spent in the area killing things, camping out, and so forth. So I can readily believe the game takes place over a year, but three years seems a bit of a stretch since there is no corroborating dialog to help us along.
This time period certainly has some interesting ramifications for the romance as well. Even if you finally get together after a year, two years is a long time to be with someone. I'd say that is a firmly established couple, rather than the "let's seek comfort together during a crisis" kinda vibe I typically got from the DAO romances (this is not a bad thing).
Although I shouldn't be complaining as this actually helps me with some fanfic stuff...
At any rate... I had seen this elsewhere in a thread but the person didn't have a source or anything. So, thanks OP for posting that.