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I have two questions:

1) When one says an ARMA process is 'stationary,' do they mean strongly stationary or weakly stationary?

2) Is there a quick way to find the variance of a stationary AR(2) model $$y_t = \beta_1 y_{t-1} + \beta_2 y_{t-2} + \epsilon_t?$$ The only way I can think of doing this is by multiplying by $y_t$, $y_{t-1}$ and $y_{t-2}$, taking expectations, and solving the Yule-Walker system with 3 equations and 3 unknowns. The trick for AR(1) models, where one takes expectations of both sides, doesn't slide here because you get a $\mathrm{Cov}(y_{t-1}, y_{t-2})$ term.

Thank you in advance.

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    For (1), please add some context. For (2), a direct route is to determine the sequence $(a_k)$ such that $$y_t=\sum_{k=0}^\infty a_k\epsilon_{t-k}$$ for every $t$ and to deduce $$E(y_t^2)=\sum_{k=0}^\infty a_k^2$$ The sequence $(a_k)$ is uniquely determined by the conditions that $a_0=1$, $a_1=\beta_1$, and, for every $k\geqslant2$, $$a_k=\beta_1a_{k-1}+\beta_2a_{k-2}$$ – 2017-01-17

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