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Mathematical Genesis of the Spatio-Temporal Covariance Functions

Author

Listed:
  • Fernández-Avilés, G
  • Montero, JM
  • Mateu, J

Abstract

Obtaining new and flexible classes of nonseparable spatio-temporal covariances have resulted in a key point of research in the last years within the context of spatiotemporal Geostatistics. Approach: In general, the literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Results: By exploring mathematical properties of positive definite functions and their close connection to covariance functions we are able to develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Conclusion/Recommendations: The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.

Suggested Citation

  • Fernández-Avilés, G & Montero, JM & Mateu, J, 2011. "Mathematical Genesis of the Spatio-Temporal Covariance Functions," MPRA Paper 35874, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:35874
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    File URL: https://mpra.ub.uni-muenchen.de/35874/1/MPRA_paper_35874.pdf
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    References listed on IDEAS

    as
    1. Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
    2. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
    3. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    4. P. Gregori & E. Porcu & J. Mateu & Z. Sasvári, 2008. "On potentially negative space time covariances obtained as sum of products of marginal ones," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 865-882, December.
    5. Montserrat Fuentes, 2002. "Spectral methods for nonstationary spatial processes," Biometrika, Biometrika Trust, vol. 89(1), pages 197-210, March.
    6. Gneiting T., 2002. "Nonseparable, Stationary Covariance Functions for Space-Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 590-600, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Spatial anisotropy; bernstein and complete monotone functions; spatio-temporal geostatistics; positive definite functions; space-time modeling; spatio-temporal data;

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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