Classes of compactly supported covariance functions for multivariate random fields

  • Daryl J. Daley
  • Emilio PorcuEmail author
  • Moreno Bevilacqua
Original Paper


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.


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

Mathematics Subject Classification

60G55 60K35 



The authors are grateful to a Referee and to the Associate Editor for their thorough reports which allowed for a considerably improved version of the manuscript. Moreno Bevilacqua acknowledges the Project “Fondecyt Iniciación”. Emilio Porcu has been supported by the Grant “Rientro Cervelli” from Regione Sardegna and now by Fondecyt Regular from Chilean Ministry of Education. Daryl J. Daley’s work was done while visiting the Universities of Sassari, Ciudad Real, Valparaiso and Federico Santa Maria.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Daryl J. Daley
    • 1
  • Emilio Porcu
    • 2
    Email author
  • Moreno Bevilacqua
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia
  2. 2.Department of MathematicsUniversidad Federico Santa MariaValparaísoChile
  3. 3.Department of StatisticsUniversidad de ValparaisoValparaísoChile

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