The Distribution and Quantiles of the Sample Mean from a Stationary Process

Edgeworth–Cornish–Fisher expansions are hugely important, as they give the distribution, density and quantiles of any standard estimate. Here we show that the sample mean of a univariate or multivariate stationary process is a standard estimate, so that all the known results for standard estimates can be applied. We also show how to allow for missing data and weighted means.