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Spatio-temporal generalized complex covariance models based on convolution

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  • De Iaco, S.

Abstract

Modeling covariance functions, with values on a complex domain, is essential for geostatistical interpolation or stochastic simulation of complex-valued random fields in space or space-time. However, little has been done for complex spatio-temporal modeling. For this aim, the construction of new classes of spatio-temporal complex-valued covariance models, based on convolution, is provided. Indeed, starting from the Lajaunie and Béjaoui models extended to a space-time domain, generalized families of complex models are obtained through the integration with respect to a positive measure. A procedure for fitting the two parts of the spatio-temporal complex models and for defining the density function considered for the integration is also illustrated. The computational details of this procedure are discussed through a case study on a spatio-temporal dataset of sea currents and the performance of these classes of models is assessed.

Suggested Citation

  • De Iaco, S., 2023. "Spatio-temporal generalized complex covariance models based on convolution," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:csdana:v:183:y:2023:i:c:s0167947323000208
    DOI: 10.1016/j.csda.2023.107709
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    References listed on IDEAS

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    1. Iaco, S. De & Myers, D. E. & Posa, D., 2001. "Space-time analysis using a general product-sum model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 21-28, March.
    2. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    3. Sandra De Iaco, 2023. "Families of complex‐valued covariance models through integration," Environmetrics, John Wiley & Sons, Ltd., vol. 34(3), May.
    4. Alexandre Rodrigues & Peter J. Diggle, 2010. "A Class of Convolution‐Based Models for Spatio‐Temporal Processes with Non‐Separable Covariance Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 553-567, December.
    5. 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.
    6. de Iaco, Sandra, 2017. "The cgeostat Software for Analyzing Complex-Valued Random Fields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i05).
    7. Felipe Tagle & Marc G. Genton & Andrew Yip & Suleiman Mostamandi & Georgiy Stenchikov & Stefano Castruccio, 2020. "A high‐resolution bilevel skew‐t stochastic generator for assessing Saudi Arabia's wind energy resources," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
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