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$$y_t=5+ε_t, ε_t |I_(t-1)~N(0,σ_t^2 ),σ_t^2=σ^2 y_t^2$$

Is this process weakley stationary?

How can I tell?

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  • $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. Please add the [self-study] tag and read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$ – jbowman May 29 '18 at 12:45
  • $\begingroup$ @jbowman Thanks for the introduction, I know that this is the constant model, I know that it would be stationary by itself, but I get confused with the sigmat^2, will this impact the stationarity of the equation? $\endgroup$ – user22485 May 29 '18 at 13:15
  • $\begingroup$ @jbowman does that answer work from your experience? $\endgroup$ – user22485 May 29 '18 at 13:25
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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.

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