Writing ARIMA model with estimation

[ecokid]

Hello,

I have a problem regarding how to write the estimate of ARIMA model and I would be really grateful if anyone could provide any help regarding it.
1. My variable is X. As I have found it non stationary in the level, so I have taken first difference of it. So it has become d(x). Now I'm using ARIMA modeling. My dependent variable is d(x) and the regressors that I've found significant are AR(1),AR(2), MA(1), MA(2). The coefficient of AR(1)=-1.13, AR(2)= -0.34,MA(1)=1.54,MA(2)=0.85. So when I am going to extend this model into lagged values of x and error terms, then how should I write it? For example should I write the above model like below:

X_t - X_t-1= -1.13 (X_t-1)-0.34 (X_t-1+X_t-2)+1.54 (e_t-1)+ 0.85 (e_t-1+e_t-2)+et
X_t= -0.47 X_t-1-0.34 X_t-2+ 2.39 e_t-1+ 0.85 e_t-2+ e t

2. Some books mention it is conventional to put negative sign before MA process. Then should I use negative sign like MA(1)=-1.54, MA(2)=-0.85 ?

Thanks for your time.