How can I form ARIMA equation given MA and AR terms 
Above is output from SAS. 
What would be the corresponding ARIMAX equation?  I would appreciate if someone could help me write the mathematical equation, preferably in the following form:
$$
Y(t)= ay(t-1) + by(t-2) + \ldots + z
$$
where $a, b, c$ are the coefficients, and $z$ is any error term.
 A: From what I know of the ARIMA model (please correct me anyone if I'm wrong) is that it is equivivalent to "pre-filter" (differencing) the data $y(t)$ and set $y_{new}(t) = y(t)-y(t-1)$. Then fit an ARMA model to this new data. This would mean your ARMA model:
\begin{equation}
y_{new}(t) = (1-q^{-1}) y(t) = \frac{C}{A}e(t),
\end{equation}
where $q^{-1}$ is the difference operator $q^{-1}y(t) = y(t-1)$ and $e(t)$ is noise.
This means you get the model (in $y$) as 
\begin{equation}
(1 - q^{-1})(1+a_1q^{-1}+\ldots+a_{n_a} q^{-n_a})y(t) = (1 + c_1 q^{-1} + \ldots + c_{n_c} q^{-n_c})e(t).
\end{equation}
A: 
Your model and coefficients expressed as a pure AR model (up to lag 12)  is here.
The equation is  multiply 1.0  time the last value and add it to
             1.15404 times the last value and add it to

            - .73264 times the value 2 periods ago and add it to

              .465   times the value 3 periods ago

          etc....

This means that the ARMAX Polynomial can be expressed as an infinite AR polynomial ... shown here to lag 12 . The coefficients are your a,b,c ...etc     
     a,b,c 


