Hello,
I know it has been four years since this question was done, and 2 years since the last comment. Nevertheless, I think it is worth answering this. You can indeed make a prediction for a new data set without having any target outputs.
One of the characteristic elements of NARX are the input delays. In order to get a good prediction in a new test set you just need a number of output targets equal to the input delays of your network (1 or 2 might be enough in most cases). If you do not have any target outputs (T) at all, you can put a random cell array including only 'zeros' or 'ones' (or some initial values that seem good enough). The initial predictions of the time series will probably not be good, but sooner or later the impact of the 'bad' initial values will diminish and the NARX will start giving good results again.
In the next figure a trained closed loop NARX was used to predict a new testing time series (2900 sec) that its target outputs were known to me. In the first instance (blue line) instead of the available target outputs I used some random values (ones). I the next case (orange) I used the correct output values for the first two seconds and then, used the same random values as before. The orange line predicted the results really good, while the blue and orange line converge after approx. 1000 sec. So your best shot is to utilize a few initial target values that are logical enough and let NARX do the rest.
I hope this helps.
All best
Georgios
PS When using the typical commands to make a predicytion with a closed loop NARX, T is your target goals:
net = closeloop(net);
view(net)
[Xs,Xi,Ai] = preparets(net,X,{},T);
y = net(Xs,Xi,Ai);
