AR(2): Xt = .3 X_{t-1} + .1 X_{t-2} + Wt. 

ø(B) Xt = Wt. 

What is ø(B)? 

ø(B) = 1 - .3B - .1B^2. 

Because (1 - .3B - .1B^2) Xt 
= Xt - .3 X_{t-1} - .1 X_{t-2} 
= Wt. 

B(X_t) = X_{t-1}, for all t.  

B^2(Xt) = B (BXt) = B(X_{t-1}) = X_{t-2}. 

Imagine considering f the function of z that corresponds to ø. 

ø(B) = 1 - .3B - .1B^2, 

then it is natural to think about the corresponding function being 

f(z) = 1 - .3z - .1z^2. 

ø is a function of B. 

f is a function of z. 

The inverse of the function ø, when it is invertible, is called psi.