Is Your Time Series Stationary or Not?

[osiris40]

Hello, I'm trying to solve this, any idea please?

Basically: Demonstrate for the next three processes if the Time Series would be stationary, if not, it should establish the conditions for it to be stationary.

Thanks

 

[DrClaude]

You'll have to show us what you have tried.

 

[HallsofIvy]

Also, are $$\phi$$ and $$\theta$$ just numbers? I assume that $$\epsilon_n$$ is a given time-series. Is that correct?

Do you understand that the question does NOT ask you to solve the equations, just determine the conditions under which the solution is "stationary"- constant. For example, the second equation, $$Y_t= \epsilon_t+ \theta \cdot \epsilon_{t-1}$$ has $$Y_n$$ stationary if and only if $$\epsilon_ t$$ is itself stationary,