Can a Variable Be Both Dependent and Independent? 
We can see that the GDP growth, represented by "y" is the dependent variable and independent variable. I would like to perform quantile regression in Eviews, with y = FC + y + c , and the coefficient for y is 1, which make sense. Do I have to do something like  y(+4) = FC + y + c if I wish to get the h quarter ahead?

The notation is discussing two different time periods.
$y_t$ refers to the GDP at some time $t$.
$y_{t+q,b}$ refers to the GDP at some other time.
These are measurements of different quantities.
