I have three questions regarding the difference between a closed-loop and an open-loop narxnet, and it's behavior.
First, a little about the problem I'm trying to solve. I have an 2xN dimensional matrix of observation (X), from which I'm trying to predict an output Y, 1xN. Now, a narxnet takes as input both X and Y. The Matlab documentation says that an open-loop narxnet finds a function 'f' where y(t) = f( y(t-1), y(t-2), x(t-1), x(t-2) ), for a delay of 2. However, the results that I get are much more accurate than I expect them to be. This suggests that the narxnet uses the actual y(t) as input as well. When I convert the open-loop to a closed-loop, and retrain it, I get much more reasonable results, not good, but reasonable.
1.a) What is the actual input to an open-loop narxnet, and the closed-loop. When trying to predict y(t), are the inputs [ y(t), y(t-1), y(t-2), x(t-1), x(t-2) ] or [ y(t-1), y(t-2), x(t-1), x(t-2) ], for both?
1.b) For my problem I need the inputs to be [ y(t-1), y(t-2), x(t), x(t-1), x(t-2) ], 0 to 2 delays on the X, and 1 to 2 delays on the Y. How can I do that?
2. For comparison, I've trained my open-loop, and tested it, then convert the open-loop to a closed-loop using
netc = closeloop(net);
then trained the closed-loop from scratch and tested it. I've read on MATLAB Answers that I should start training the closed-loop with the weights from the open-loop net. How can I used the weights of one net as the initial weights for training another?
3. I understand that the narxnet uses a combination of NNs and difference equations. I problem I run into when using a closed-loop narxnet is that my predictions begin to oscillate and explode exponential. I know that this problem occurs in a difference equation, such as y(t)=a*y(t-1)+b, when 'a' is greater than 1. What, in a closed-loop narxnet could cause this similar issue?
I didn't include any code because my questions need high-level understanding and explanations, which I am lacking.
A huge thank you in advance,