A new class of spatial covariance functions generated by higher-order kernels

TL;DR

This paper introduces a novel class of spatial covariance functions derived from higher-order kernels via Fourier transforms, extending them to spatio-temporal data, enhancing modeling flexibility.

Contribution

The paper presents a new method for constructing spatial covariance functions using higher-order kernels and extends this approach to spatio-temporal datasets.

Findings

New class of covariance functions introduced

Extended to spatio-temporal settings

Potential for improved spatial modeling

Abstract

Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier transform of some higher-order kernels. Further, we extend this class of the spatial covariance functions to the spatio-temporal setting by using the idea used in Ma (2003).