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,