# How do you express ARIMA(2,1,2) in terms of the backshift operator?

I've so far achieved the following:

$$y_t-y_{t-1}=\phi_1y_{t-1}+\phi_2y_{t-2}- \theta_1e_{t-1}-\theta_2e_{t-2}+e_t$$

Therefore Yt-BYt=(phi)Byt+phiB^2yt-B(theta)et-B^2(theta)et+et

Yt-BYt-(phi)Byt-phiB^2yt= et(1-Btheta-B^2 theta)

This is the part where I get stuck.

I'm sorry if this appears confusing....

• You are dropping the indices on $\phi_i$ and $\theta_j$ along the way. Please try to get acquainted with MathJax notation to make your post more readable. One further common simplification is to set $\Delta=1-B$. – Christoph Hanck Jan 11 at 15:01