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This paper proposes a model for time series based on a hierarchy of sigmoid belief networks connected through time. The recently proposed Neural Variational Inference and Learning (NVIL) framework is applied to design scalable (approximate) inference and learning in the model. The model is shown to generate bouncing balls, polyphonic music, motion capture and text. Strong points - The starting point of this paper (deep directed models, variational inference) is a popular and interesting line of research. This is one paper amid several time series extensions of this family of models/inference methods and is a natural extension of this line of work.