Suppose I have a sample of $n+m$ observations of $\{x_i,y_i\}$ and i use the first $n$ observations to estimate the parameters in my model and save the last $m$ observations for forecasting. Let $\hat{f}_{n+h} $ be the one-step-ahead forecast of $y_{n+h+1}$ for $h=0,1,..m-1$.
How do i estimate $y_{n+h+2}$ ?
Do I use the $n+1$ observations of both $x$ and $y$ to estimate $\hat{f}_{n+h+1} $
or use $n+1$ observations from $x$ and $n$ from $y$ and $\hat{f}_{n+h} $ to estimate $\hat{f}_{n+h+1} $?
Thanks