I have one question, which is related to a solution presented in "A proof for the stationarity of an AR(2)" by Christoph Hanck. Since I still cannot write comments (I need at least 50 points), maybe someone can explain to me why in this solution (and many others) we are ignoring other two inequalities, i.e. $\phi_1 - \sqrt{\phi_1^2 + 4\phi_2} < 2$ and $-2 < \phi_1 + \sqrt{\phi_1^2 + 4\phi_2}$? I understand the other two and I fully agree with the solutions from inequalities but I need some explanation with the other two (why are we just ignoring them or maybe we get the same result?). My idea was to use inequalities $|\phi_1| <2$ and $|\phi_2|<1$ in order to show that maybe the inequalities stated above give the same result as the other two. But my attempt failed (or maybe I just made a mistake using $|\phi_1| <2$ and $|\phi_2|<1$).
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