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An analytical process of spatial autocorrelation functions based on Moran’s index

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  • Yanguang Chen

Abstract

A number of spatial statistic measurements such as Moran’s I and Geary’s C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary’s coefficient and Getis’ index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.

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  • Yanguang Chen, 2021. "An analytical process of spatial autocorrelation functions based on Moran’s index," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-27, April.
    • Handle: RePEc:plo:pone00:0249589
    DOI: 10.1371/journal.pone.0249589
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    1. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
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    Cited by:

    1. Keqiang Dong & Liao Guo, 2021. "Research on the Spatial Correlation and Spatial Lag of COVID-19 Infection Based on Spatial Analysis," Sustainability, MDPI, vol. 13(21), pages 1-16, October.
    2. Fulin Liu & Shixin Ding & Jinxing Zhang & Yingying Wang, 2024. "A multiscale and multiperspective quantifying framework for spatial patterns and influencing mechanisms of geographical indications," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-12, December.

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