So, Jack is a fair weather waver. He doesn't wave at people when they're coming or going...but usually waves at the TV or out the window, and usually waves to show excitement or any other random emotion.
I'm not sure what the emotion is here, seems like a mix of everything...although I think it ends in some tired crying. But he waves like this all...the...time! And usually it's when he's excited about something...and with Cheerios, there's always at least a little excitement!