We consider the time series ARMA(2,1):
$X(t)-0.75X(t-1)+0.5625X(t-2)=Z(t)+1.25Z(t-1)$
Does $\{X(t)\}$ have stationary solution? Give the form of the solution.
At first we are looking for the roots of autoregressive polynomial. None of them is on the unit circle so the solution is stationary.
Then I don't know how to find this solution. I know it has a following form:
$X(t)=\sum_{j=-\infty}^{\infty}\Phi_jZ(t-j)$
where
$\sum_{j=-\infty}^{\infty}\Phi_jz^j=\frac{1+1.25z}{1-0.75z+0.56z}$.