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Spatiotemporal modelling using integro‐difference equations with bivariate stable kernels

Author

Listed:
  • Robert Richardson
  • Athanasios Kottas
  • Bruno Sansó

Abstract

An integro‐difference equation can be represented as a hierarchical spatiotemporal dynamic model using appropriate parameterizations. The dynamics of the process defined by an integro‐difference equation depends on the choice of a bivariate kernel distribution, where more flexible shapes generally result in more flexible models. Under a Bayesian modelling framework, we consider the use of the stable family of distributions for the kernel, as they are infinitely divisible and offer a variety of tail behaviours, orientations and skewness. Many of the attributes of the bivariate stable distribution are controlled by a measure, which we model using a flexible Bernstein polynomial basis prior. The method is the first attempt to incorporate non‐Gaussian kernels in a two‐dimensional integro‐difference equation model and will be shown to improve prediction over the Gaussian kernel model for a data set of Pacific sea surface temperatures.

Suggested Citation

  • Robert Richardson & Athanasios Kottas & Bruno Sansó, 2020. "Spatiotemporal modelling using integro‐difference equations with bivariate stable kernels," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1371-1392, December.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:5:p:1371-1392
    DOI: 10.1111/rssb.12393
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    References listed on IDEAS

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    1. Christopher K. Wikle & Scott H. Holan, 2011. "Polynomial nonlinear spatio‐temporal integro‐difference equation models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32, pages 339-350, July.
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    3. Christopher Wikle & Mevin Hooten, 2010. "Rejoinder on: A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 466-468, November.
    4. Press, S. J., 1972. "Multivariate stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 444-462, December.
    5. Robert Alan Richardson, 2017. "Sparsity in nonlinear dynamic spatiotemporal models using implied advection," Environmetrics, John Wiley & Sons, Ltd., vol. 28(6), September.
    6. Richardson, Robert & Kottas, Athanasios & Sansó, Bruno, 2017. "Flexible integro-difference equation modeling for spatio-temporal data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 182-198.
    7. Tilmann Gneiting & Larissa Stanberry & Eric Grimit & Leonhard Held & Nicholas Johnson, 2008. "Rejoinder on: Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 256-264, August.
    8. Tilmann Gneiting & Larissa Stanberry & Eric Grimit & Leonhard Held & Nicholas Johnson, 2008. "Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 211-235, August.
    9. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
    10. Xu, Ke & Wikle, Christopher K. & Fox, Neil I., 2005. "A Kernel-Based Spatio-Temporal Dynamical Model for Nowcasting Weather Radar Reflectivities," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1133-1144, December.
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    Cited by:

    1. Li, Yunzhe & Lee, Juhee & Kottas, Athanasios, 2024. "Bayesian nonparametric Erlang mixture modeling for survival analysis," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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