Sequence prediction for single vs multiple data streams

Not 100% sure how to explain this, but I am searching for ideas for prediction in a sequence.

For a single sequence of numbers, I want to predict missing (or incorrect) values. An RNN could probably do this, but what are other possible methods?

More interestingly, what should one do if there are multiple streams of data - which may or may not be correlated? Are there any good methods for exploiting possible correlation to improve efficiency?