$$y_t=5+ε_t, ε_t |I_(t-1)~N(0,σ_t^2 ),σ_t^2=σ^2 y_t^2$$
Is this process weakley stationary?
How can I tell?
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The process above shows a constant model with some ARCH/GARCH type conditional variance.
The important thing to note is that the definition of weak stationarity in terms of variance is that the unconditional variance is constant. Here it is, and it also meets the other two stationarity conditions.
The trick in the question is that the ARCH/GARCH type errors are only concerned with the conditional variance. Therefore, to answer the questions, ignore the conditional variance component, and conclude that it is weakly stationary.