Do not worry if your baby does not imitate you initially. Continue to imitate your baby's actions and add your own. Your baby should be able to imitate you by the time they turn six to eight months old.
Researchers have posited that mirroring back behaviour is emotionally pleasing to infants and facilitates further communication.
Recent studies have found that imitation is not an innate behaviour but one that is learned in babies' first months. One possibility is that babies learn to imitate other people by watching other people imitate them. Another study from the same lab found that parents imitate their babies once every two minutes on average. Hence, adults imitating babies could be a powerful means by which infants learn to link their gestures with those of another person.
Read more at CD-PLY-C01 and CD-PLY-C02.