COMPARISON OF SOME METHODS TO ESTIMATE THE LIMITING VALUE OF THE VARIOGRAM, V(H)(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 upsilon(k)(j) for Sampling interv al j=0. These methods and the method where the modified cubic spline i s used for the modeling of the variogram and the auxiliary functions c alculated from it are compared in this study. The methods are tested w ith simulated time series and with time series from the pulp bleaching process. Gy's two methods, which need an additional experiment at a s hort time interval, proved to be superior compared to the other method s even for the periodic time series. If only one time series is availa ble the graphical estimation and the methods proposed in this study ca n be used. These methods are comparable when nu(h)(0) is 10% Or more f rom than the long range variation in the time series. When nu(h)(0) is less than 10% from than the long range variation in the time series t he method proposed in this study is as an average better than the grap hical estimation. In addition, especially for periodic processes, nu(h )(0) should be estimated graphically.