0
$\begingroup$

I know that a finite MA process $X_t = \Theta(B)Z_t$ is always stationary.

Also, whether an AR(p) process is stationary or not can be verified by checking the roots of $\Phi(B)=0$ where the process is $\Phi(B)X_t=Z_t$.

Consequently, we can also check if an ARMA(p, q) process is stationary or not by checking the roots of $\Phi(B)=0$ where the process is $\Phi(B)X_t=\Theta Z_t$.

But how to check if an ARIMA (p,d,q) process is stationary or not?

Let the ARIMA process be $\Phi(B).(1-B)^d.X_t=\Theta(B).Z_t$

Do I need to compute the roots of $\Phi(B).(1-B)^d=0$ or just the roots of $\Phi(B)=0$ in order to determine stationarity?

$\endgroup$
  • $\begingroup$ $\Phi(B).(1-B)^d=0$ already has $d$ roots equal to $1$. That's why we pull them out. To further check whether still any unit root is left you just need to check the roots of $\Phi(B)=0$. $\endgroup$ – Dayne Oct 16 at 5:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.