given causal ARMA process $Xt$, find PACF: $X(t) - cX(t-1) - c^2X(t-2) = Z(t)$
$1 - cz - c^2z^2 = 0, $
$ z= \frac{-1 + \sqrt{5}}{2a}$
and
$z= \frac{-1 - \sqrt{5}}{2a}$
My book (Introduction to Time Series, Brockwell & Davis) defines every alpha as an AR coefficient as seen below. So would that just follow that $α(1)=c$ and $α(2)=c^{2}$ ?
However, the solutions I found online are not consistent with this:
Edit: I did calculate everything through and my book is correct, - the alphas are just AR(p) coefficients. I would be curious to know why it was not the case for the other problem above.