There has been some work on adapting deep learning methods for sequential data. A lot of this work has focused on developing "modules" which can be stacked in a way analogous to stacking restricted boltzmann machines (RBMs) or autoencoders to form a deep neural network. I'll highlight a few below:


Conditional RBMs: Probably one of the most successful applications of deep learning for time series. Taylor develops a RBM like model that adds temporal interactions between visible units and apply it to modeling motion capture data. Essentially you end up with something like a linear dynamical system with some non-linearity added by the hidden units.
Temporal RBMs: In his thesis (section 3) Ilya Sutskever develops several RBM like models with temporal interactions between units. He also presents some interesting results showing training recurrent neural networks with SGD can perform as well or better than more complex methods, like Martens' Hessian-free algorithm, using good initialization and a slightly modified equation for momentum.
Recursive Autoencoders: Lastly I'll mention the work of Richard Socher on using recursive autoencoders for parsing. Although this isn't time series, it is definitely related.


Using deep learning for time series prediction
I'm looking for a Windows GUI tool to compare the contents of two folders and show which files are different....
