Contours and dimple for the Gneiting class of space-time correlation functions

F. Cuevas, E. Porcu, M. Bevilacqua

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We offer a dual view of the dimple problem related to space-time correlation functions in terms of their contours.We find that the dimple property (Kent et al., 2011) in the Gneiting class of correlations is in oneto-one correspondence with nonmonotonicity of the parametric curve describing the associated contour lines. Further, we show that given such a nonmonotonic parametric curve associated with a given level set, all the other parametric curves at smaller levels inherit the nonmonotonicity. We propose a modified Gneiting class of correlations having monotonically decreasing parametric curves and no dimple along the temporal axis.

Original languageEnglish
Pages (from-to)995-1001
Number of pages7
Issue number4
StatePublished - 1 Dec 2017


  • Dimple
  • Gneiting correlation function
  • Isoline
  • Random field


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