Math.Expectation And Variance of Stationary Series

Question

we have formula of stationary time series $$y_t = 0.6\cdot y_{t-1} + 2 + e_t$$ as mathematical expectation is constant, we can do the following: $$E = 0.6\cdot E + 2 + 0$$ $$E = 5$$ Variance is $\sigma^2 = E(y_t^2)-(E(y_t))^2 = E(y_t^2)-25$

1. Is it correct?
2. How to calculate variance until the end?

Answer 1

The mean is correct. You can use the same methodology to compute the variance:$$\begin{align*}\sigma^2 &= V(y_t) \\&= V(0.6\cdot y_{t-1} + 2 + e_t) = 0.6^2\sigma^2 + V(e_t)\end{align*}.$$ Solving for $\sigma^2$ yields $\sigma^2=V(e_t)/0.64$