A parametric variogram model bridging between stationary and intrinsically stationary processes

TL;DR

This paper introduces a flexible two-parameter variogram model that unifies several existing models and smoothly transitions between stationary and intrinsically stationary processes, enhancing spatial data modeling capabilities.

Contribution

A novel parametric variogram model that bridges stationary and intrinsically stationary processes within a Gaussian framework and for spatial extremes modeling.

Findings

Includes power variogram for fractional Brownian motion

Encompasses modified De Wijsian, generalized Cauchy, and multiquadrics models

Allows smooth transition between different process types

Abstract

A simple variogram model with two parameters is presented that includes the power variogram for the fractional Brownian motion, a modified De Wijsian model, the generalized Cauchy model and the multiquadrics model. One parameter controls the smoothness of the process. The other parameter allows for a smooth parametrization between stationary and intrinsically stationary second order processes in a Gaussian framework, or between mixing and non-ergodic max-stable processes when modeling spatial extremes by a Brown-Resnick process.