EDIT: I figured out the problem I was having with Eqn 4.3.31 on pg. 76. I was making an algebra error.

We have γ0 = φ1*γ1 + φ2* γ2 + ... + φp*γp + (σe)^2

Since ρk = γk / γ0, we can substitute ρk*γ0 for γk in the equation above.

γ0 = φ1*ρ1*γ0 + φ2*ρ2*γ0 + ... + φp*ρp*γ0 + (σe)^2

<=> 1 = φ1*ρ1 + φ2*ρ2 + ... + φp*ρp + (σe)^2 This is wrong!

Instead it should be

γ0 = φ1*ρ1*γ0 + φ2*ρ2*γ0 + ... + φp*ρp*γ0 + (σe)^2

<=> γ0 – φ1*ρ1*γ0 – φ2*ρ2*γ0 – ... – φp*ρp*γ0= (σe)^2

<=> γ0 (1 – φ1*ρ1 – φ2*ρ2 – ... – φp*ρp) = (σe)^2

<=> γ0 = (σe)^2 / (1 – φ1*ρ1 – φ2*ρ2 – ... – φp*ρp)