Anna to the Infinite Power (1983)

Anna Hart was always an odd child, a genius, a shoplifter, desperately afraid of flickering lights, with strange prophetic dreams. Simultaneously, several strange things begin to happen. A strange, mysterious neighbor, by the name of MacKayla moves in next door to the Harts. And, most frightening of all, Anna sees her exact double on the television one night. As her investigation of the other Anna, Anna Smithson, progresses, she begins to learn the truth. The truth about a woman named Anna Zimmerman that has been dead for twenty years, and most importantly, the truth about herself.