Comparison of some methods to estimate the limiting value of the variogram, vh(j), for the sampling interval j=0 in sampling error estimation

The variogram as a function of the sampling interval can be calculated from the time series measurements. P. Gy has proposed some methods to estimate the value of the variogram vh(j) for sampling interval j=0. These methods and the method where the modified cubic spline is used for the modeling of the variogram and the auxiliary functions calculated from it are compared in this study. The methods are tested with simulated time series and with time series from the pulp bleaching process. Gyʹs two methods, which need an additional experiment at a short time interval, proved to be superior compared to the other methods even for the periodic time series. If only one time series is available the graphical estimation and the methods proposed in this study can be used. These methods are comparable when vh(0) is 10% or more from than the long range variation in the time series. When vh(0) less than 10% from than the long range variation in the time series the method proposed in this study is as an average better than the graphical estimation. In addition, especially for periodic processes, vh(0) should be estimated graphically.