Asymptotic confidence intervals for variograms of stationary time series

Industrial processes are often monitored via data sampled at a high frequency and hence are likely to be autocorrelated time series that may or may not be stationary. To determine if a time series is stationary or not the standard approach is to check whether sample autocorrelation function fades out relatively quickly. An alternative and somewhat sounder approach is to use the variogram. In this article we review the basic properties of the variogram and then derive a general expression for asymptotic confidence intervals for variogram based on the Delta method. We illustrate the computations with an industrial process example.