In my forecasting textbook coauthored with George Athanasopoulos, we provide formulas for the forecast variances of four simple benchmark forecasting methods, but we don’t explain where they come from. So here are the derivations.

We assume that the residuals from the method are uncorrelated and homoscedastic, with mean 0 and variance . Let <img src=“https://latex.codecogs.com/png.latex?y_1,%5Cdots