NARX customization of training algorythms

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Hello everyone!
Can someone explain more about customizing of NARX networks training algorithms in Matlab? I read everything that was in the help, studied the various parameters of training function, but there are more questions than answers. Can you elaborate on what you can change in the functions of a network training and most importantly - what these changes affects? If it is possible, with the specific code of parameters in Matlab as examples.
I would also like to know whether there are some standard steps that are applicable to training NARX network for any task? For example, I met a few times things like "addition of a RNG initialization statement" and others. How can I add this and whether there are some important things that you should pay attention to?
Currently by using the standard functions with a few changes I get the same negative results. Training ends very quickly and "finds optimal value", however, when I start the network, result is essentially a shift of an input graph by one step to the right with a few changes, as you can see in picture
I think that the problem is to set up a learning algorithm, but, unfortunately, I do not know which side to start to solve the problem - any changes that I was trying to make lead to similar results.
Most likely, someone faced similar problems, and I would be very grateful if someone could tell more about customizing of learning algorithms.
Thanks in advance!

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