After having the LOUDEST parrot in the history of creation, I researched everything to do for them. Not that it worked for MINE of course, LOL...but he was too spoiled from the get-go, so it's my own fault. One thing that the "experts" say to do, is to put him in his cage and go out of the room. Even if you're only out for a second, and he doesn't scream, go back in and give him a treat and praise him. Supposedly, if you do this over and over, and extend the times that you're out of the room, but try to go back BEFORE he starts squawking, he'll learn to be quiet while you're out of the room, b/c he knows that he'll get a treat when you return. So you have to be consistent with it and always give him a treat when you return (IF he's been good). There's a book you can get probably at Petco or Petsmart called something like "The Well-behaved Parrot".....you might look thru it and see if it might help. I was so lucky; I lived in an apartment complex for 14 years on the bottom floor at the end, always had people living above me and not once did anyone complain about my bird screaming; I had 2 of them, but at least the female was slightly more sedate (and I'm not joking about him being the loudest....here's a link to what he could have sounded like if he were just a teensy bit quieter
http://www.mytoos.com/. Hopefully your neighbors are gone during the day when he does most of his vocalizing or when they're home in the evenings they have music or the tv on.