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Mathematical Genesis of the Spatio-Temporal Covariance Functions

Author

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  • 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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    References listed on IDEAS

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    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.
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    Cited by:

    1. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, January.

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    More about this item

    Keywords

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

    JEL classification:

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

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