Stationarity condition for specific Autoregressive AR(2) Process: $y_{t} = y_{t-1} + Cy_{t-2} + z_{t}$ The Autoregressive (AR) process $y_{t} = y_{t-1} + Cy_{t-2} + z_{t}$ is stationary provided that $-1 < C < 0$.
We know that a general AR(2) process i.e., $y_{t} =  a_1 y_{t-1} + a_2 y_{t-2} + z_{t}$, the stationary conditions are

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*$a_1 + a_2 < 1$

*$a_2 - a_1 < 1$

*$|a_2| < 1$
By following these conditions we get following conditions for our particular AR(2) model.

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*$C < 0$

*$C < 2$

*$-1 < C < 1$
My question is why we take minimum value of $C$ from upper limits of above conditions on $C$ i.e, $\min(0,1,2)$ in $-1 < C < 0$?

Because the intersection of these three conditions is $-1<C<0$, i.e.
$$\{C|(C<0) \cap (C<2) \cap (-1<C<1)\}=\{C|-1<C<0\}$$
