Is moodiness genetic?

Can be. Depends on the type of moodiness. Teenage moodiness probably is more environmentally induced that genetic. However, many causes of persistent moodiness--depression, dysthymia, anxiety, and bipolar disorder, e.g.--all have genetic contributions. That said, genes are only a part of the picture, and predisposition does not mean it has to happen. If it's causing problems, seek help.