Researchers at Stanford University released this paper in 2012:
It goes on to discuss how they used echo state networks to predict things such as Google's stock prices. However to do this once trained, the network's inputs are a day's stock price, and the output is the day's predicted stock price. The way the paper is worded is like this could be used to predict future stock prices for example. However, to predict tomorrows stock price, you need to give the neural network tomorrows stock price...
All this paper seems to show is that the neural network is converging on a solution where it simply modifies its inputs a minimal amount, hence the output of the ESN is just a small alteration of its input.
Here are some Python implementations of the work shown in this paper:
In particular, I was playing with the latter which produces the following graph:
If I take the same trained network, and alter the 7th's day's "real" stock price to say something extreme like $0, this is what comes out:
As you can see, it basically regurgitates its inputs. So, what is the significance of this paper? It has no use in any financial predictions like the network shown in this paper: