Oreimo

Kousaka Kyousuke, a normal 17-year-old high school student living in Chiba, has not gotten along with his younger sister Kirino in years. For longer than he can remember, Kirino has ignored his comings and goings and looked at him with spurning eyes. It seemed as if the relationship between Kyousuke and his sister, now fourteen, would continue this way forever. One day however, Kyousuke finds a DVD case of a magical girl anime which had fallen in his house's entrance way.

(Source: Crunchyroll)