I've been attempting to do multi-step ahead prediction with the NARX (Non-Linear with Exogenous Inputs) Neural Network. As I understand it, this network can be defined mathematically as follow:

$y(t+1) = F(y(n), ..., y(n-q+1), u(n), ..., u(n-q+1))$

Where the size of the tapped delay line memory is represented by $q$. So in order to do a 1-step ahead prediction, the network simply takes as input the current and past values of the exogenous function $u(n)$ as well as the current and past values of the time-series I am interested on $y(t)$.

Now suppose that I want to predict all the values from $y(t+1)$ to $y(t+10)$, how would I go about doing this? It seems that I need the current value of the exogenous time-series $u(n)$ at each time-step however this is not available to me. Am I missing something here? I would greatly appreciate if anyone can point me in the right direction.


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