Assume $e_i=(\epsilon_i+\epsilon_{i+1})/2, i=1,...,n$ where $\epsilon_1,...,\epsilon_{n+1}$ are iid with mean zero and variance $\sigma^2$. Then $e_i$ are the moving average errors. Now, consider the model $Y_i=\mu+e_i, i=1,...,n$. I want to show two statements: 1. $$E(Y_{i+1}|Y_1,...,Y_i)=\frac{...