The average age for
waving "bye" back to someone who waved to him is 10 months.
At that age a baby should mimic "Pat-a-Cake & "Peek-a-Boo", raise his arms to be picked up (6-9 mos.) & turn consistently to his name. (8-9 mos.) These are signs of reciprocal social communication & reciprocal social interaction. If absent, seek an assessment by your state's Early Intervention Program for Autistic Spectrum Disorder.