On the use of variograms for the prediction of time series

We consider the prediction of stationary stochastic processes with non-zero mean. When the covariance of the process is known, but the mean is not, the classical approach is to first estimate the mean from the past data, and then apply an optimal predictor to the zero-mean residuals. Bastin and Henriet [1] showed that an alternative was to use a predictor based on ‘variograms’ rather than covariance information, thus avoiding the estimation of the mean. We show here that the two predictors are identical when the unknown mean is replaced by its minimum variance estimate. We also examine, through simulation, how the two predictors compare when the statistics are unknown.