Why are RNNs better than MLPs at predicting time series data? Understandably RNNs are very good at solving problems involving audio, video and text processing due to the arbitrary input's length of this sort of data.
What I don't understand is why RNNs are also superior at predicting time series data and why we use them over simple MLP DNNs.
Say I wanted to predict what the value in the time series is at $t+1$. I would take a window of, let's say, $t-50, t-49, \dots, t$, and then feed loads of sampled training data into a network. I could either choose to have a single LSTM unit remembering the entire window and basing the predictions on that, or I could simply make a 50 neuron wide MLP network.
What exactly is it about RNNs that makes them better in this scenario or any scenario for that matter?
I understand that the LSTM would have substantially fewer weights (in this scenario) and should be less computationally intensive, but, apart from that, I don't see any difference in these two methods.
In an RNN, the output of the previous state is passed as an input to the current state. Intuitively, there is a temporal (time-based) relationship in the way in which input is processed in an RNN. It can understand how the current state was achieved on the basis of the previous values, i.e value at time-step $t$ is a result of value at time-steps $t-1, t-2$, and so on.
In a DNN, there is no temporal relationship in the way input is processed. Values at time-steps $t, t-1, t-2, \dots $ are all treated distinctly and not as a continuation of the previous time-step values.