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A parametric model bridging between bounded and unbounded variograms
Author(s) -
Schlather Martin,
Moreva Olga
Publication year - 2017
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.134
Subject(s) - variogram , mathematics , fractional brownian motion , bounded function , ergodic theory , parametric statistics , gaussian process , mixing (physics) , statistical physics , cauchy distribution , gaussian , mathematical analysis , brownian motion , statistics , kriging , physics , quantum mechanics
A simple variogram model with two parameters is presented that includes the power variogram for fractional Brownian motion, a modified De Wijsian model, the generalized Cauchy model and the multiquadric model. One parameter controls the sample path roughness of the process. The other parameter allows for a smooth transition between bounded and unbounded variograms, that is, between stationary and intrinsically stationary processes in a Gaussian framework, or between mixing and non‐ergodic Brown–Resnick processes when modeling spatial extremes. Copyright © 2017 John Wiley & Sons, Ltd.