ARMAX model for discrete inputs

Hi,

I would like to know if it is possible to use system identification theory in order to derive an ARMAX model for a system that accepts inputs from a discrete group (for example u(t) can only take values from this {1,2,3, ... n} where n is finite) and the output is a real number (y(t) is a real number).

I know how to do system identification in the case where u(t) is also a real number but I don't know if the theory holds in the case when u(t) has discrete values.

Thank you.