So given an MA(2) model : Xt = Wt + Theta1 * Wt-1 + Theta2 * Wt-2 Where Wt is white noise. (Normally distributed) and Theta1 and theta2 were available. Say if X96,X97,...X100 of the series were given and we were to find out X101 and X102 with approximations. Do I change the model to ARMA and then proceed, if yes how? Or do I straight up implement the following dualtiy
Pi(B) * Xt = Theta(B) * Wt
Where B is back operator (B * Xt = Xt-1)
Pi(B) = 1 + Pi(1)B + Pi(2)(B^2) + ....
(1 + Theta1*B + Theta2*(B^2))*(1+Pi(1)*B + Pi(2)*(B^2)..) = 1 ----(1)
I tried this way and got stuck here. (How do we solve for all the Pi's in eqn (1) if this at all is the right way of doing it?)