Classes of compactly supported covariance functions for multivariate random fields

Daryl J. Daley, Emilio Porcu, Moreno Bevilacqua

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


The paper combines simple general methodologies to obtain new classes of matrix-valued covariance functions that have two important properties: (i) the domains of the compact support of the several components of the matrix-valued functions can vary between components; and (ii) the overall differentiability at the origin can also vary. These models exploit a class of functions called here the Wendland–Gneiting class; their use is illustrated via both a simulation study and an application to a North American bivariate dataset of precipitation and temperature. Because for this dataset, as for others, the empirical covariances exhibit a hole effect, the turning bands operator is extended to matrix-valued covariance functions so as to obtain matrix-valued covariance models with negative covariances.

Original languageEnglish
Pages (from-to)1249-1263
Number of pages15
JournalStochastic Environmental Research and Risk Assessment
Issue number4
StatePublished - 1 May 2015


  • Compact support
  • Hole effect
  • Multivariate random fields
  • Positive definite
  • Wendland–Gneiting class


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