The mutual variogram estimate of the signal processes

Abstract

The paper deals with the problem of a statistical analysis of time series connected with the estimation of mutual variogram, a measure of spatial correlation. G. Matheron has coined the term variogram, although earlier appearances of this function can be found in the scientific literature. We present the limiting expressions of the first two moments and the higher order cumulants of the classical mutual variogram estimate of the second-order-stationary stochastic process with discrete time. These expressions are then used to prove the theorem concerning the asymptotic distribution of the mutual variogram estimate.