From the title I'm supposed to show $\bar{y} \rightarrow \mu$ (converges in probability) where $y_t = \mu + u_t$ $ u_t = \rho u_{t-2} + \epsilon_t$$ E(\epsilon) = 0, E(\epsilon^2) = \sigma^2, E(\epsilon_t\epsilon_s) = 0, 0 \leq \rho \leq 1$ So I'm not sure if my math is right, but If i show that $\bar{y} = \frac{1}{N}\sum (\mu + u_t) = \frac{1}{N}N\mu+\sum u_t $ and $\sum u_t $ goes to 0 will that be enough?
I can show each term of $\sum u_t$ will include a $\epsilon_t$ which the ExpValue is 0. But I'm not sure if that's enough.
I'm mildy mathematically mature finance grad student in my first econometrics class so any help would be really appreciated. Thanks.