A multiscale measure of spatial dependence based on a discrete Fourier transform

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3 Scopus citations


The measurement of spatial dependence within a set of observations or the residuals from a regression is one of the most common operations within spatial analysis. However, there appears to be a lack of appreciation for the fact that these measurements are generally based on an a priori definition of a spatial weights matrix and hence are limited to detecting spatial dependence at a single spatial scale. This paper highlights the scale-dependence problem with current measures of spatial dependence and defines a new, multi-scale approach to defining a spatial weights matrix based on a discrete Fourier transform. This approach is shown to be able to detect statistically significant spatial dependence which other multi-scale approaches to measuring spatial dependence cannot. The paper thus serves as a warning not to rely on traditional measures of spatial dependence and offers a more comprehensive, and scale-free, approach to measuring such dependence.

Original languageEnglish (US)
Pages (from-to)849-872
Number of pages24
JournalInternational Journal of Geographical Information Science
Issue number5
StatePublished - 2022
Externally publishedYes


  • Fourier transform
  • Moran’s I
  • Multiscale
  • spatial dependence
  • spatial weights matrix

ASJC Scopus subject areas

  • Information Systems
  • Geography, Planning and Development
  • Library and Information Sciences


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