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Flexible integro-difference equation modeling for spatio-temporal data

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  • Richardson, Robert
  • Kottas, Athanasios
  • Sansó, Bruno

Abstract

The choice of kernel in an integro-difference equation (IDE) approach to model spatio-temporal data is studied. By using approximations to stochastic partial differential equations, it is shown that higher order cumulants and tail behavior of the kernel affect how an IDE process evolves over time. The asymmetric Laplace and the family of stable distributions are presented as alternatives to the Gaussian kernel. The asymmetric Laplace has an extra parameter controlling skewness, whereas the class of stable distributions includes parameters controlling both tail behavior and skewness. Simulations show that failing to account for kernel shape may lead to poor predictions from the model. For an illustration with real data, the IDE model with flexible kernels is applied to ozone pressure measurements collected biweekly by radiosonde at varying altitudes. The results obtained with the different kernel families are compared and it is confirmed that better model prediction may be achieved by electing to use a more flexible kernel.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:182-198
    DOI: 10.1016/j.csda.2016.11.011
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    1. 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.

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