Variogram analysis of stochastic processes

Properties of the semivariogram of an intrinsically stationary continuous-time random process with finite second moment are investigated. A necessary and sufficient conditions for a continuous function to be semivariogram are found. Confidence intervals for the semivariogram of Gaussian stationary stochastic process are defined. Properties of $\chi^{2}$-distribution are used for constructing confidence intervals for semivariogram. The proposed confidence intervals are more informative compared with point estimates of the semivariogram.