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A Simple Isotropic Correlation Family in $${\mathbb R}^3$$ R 3 with Long-Range Dependence and Flexible Smoothness

In: Research Papers in Statistical Inference for Time Series and Related Models

Author

Listed:
  • Victor De Oliveira

    (The University of Texas at San Antonio)

Abstract

Most geostatistical applications use covariance functions that display short-range dependence, in part due to the wide variety and availability of these models in statistical packages, and in part due to spatial interpolation being the main goal of many analyses. But when the goal is spatial extrapolation or prediction based on sparsely located data, covariance functions that display long-range dependence may be more adequate. This paper constructs a new family of isotropic correlation functions whose members display long-range dependence and can also model different degrees of smoothness. This family is compared to a sub-family of the Matérn family commonly used in geostatistics, and two other recently proposed families of covariance functions with long-range dependence are discussed.

Suggested Citation

  • Victor De Oliveira, 2023. "A Simple Isotropic Correlation Family in $${\mathbb R}^3$$ R 3 with Long-Range Dependence and Flexible Smoothness," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 111-122, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_4
    DOI: 10.1007/978-981-99-0803-5_4
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