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Neural-network-based generative models, such as mixture density networks, are potential solutions for speech synthesis. In this paper we follow this path and propose a recurrent mixture density network that incorporates a trainable autoregressive model. An advantage of incorporating an autoregressive model is that the time dependency within acoustic feature trajectories can be modeled without using the conventional dynamic features. More interestingly, experiments show that this autoregressive model learns to be a filter that emphasizes the high frequency components of the target acoustic feature trajectories in the training stage. In the synthesis stage, it boosts the low frequency components of the generated feature trajectories and hence increases their global variance. Experimental results show that the proposed model achieved higher likelihood on the training data and generated speech with better quality than other models when dynamic features were not utilized in any model.