This paper proposes a mixture model that considers dependence to multiple topics. In time series documents such as news, blog articles, and SNS user posts, topics evolve with depending on one another, and they can die out, be born, merge, or split at any time. The conventional models cannot model the evolution of all of the above aspects because they assume that each topic depends on only one previous topic. In this paper, we propose a new mixture model which assumes that a topic depends on previous multiple topics. This paper shows that the proposed model can capture the topic evolution of death, birth, merger, and split and can model time series documents more adequately than the conventional models.