Yes... and no. They are Jean Shepherd's Parker family seen in A Christmas Story, as well as Phantom of the Open Hearth and The Great American Fourth of July and Other Disasters, but it's also a stand-alone interpretation. You don't have to view A Christmas Story in order to understand what's happening in Ollie Hopnoodle. The characters here differ somewhat, like Ralphie has brown hair and doesn't wear glasses, Mother is a bit more ditsy, and the Old Man smokes, but Randy is pretty much exactly the same as he was in A Christmas Story. The actors were allowed to make the characters their own and not try to copy what came before.