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

Area of Science:

• Geographic Information Science
• Spatial Statistics
• Geocomputation

Background:

• Spatial autocorrelation analysis is crucial for understanding spatial patterns.
• Existing methods often adapt time series concepts to spatial data, with limitations.
• Traditional spatial statistics like Moran's I and Geary's C are foundational.

Purpose of the Study:

• To develop novel 2-dimensional spatial autocorrelation functions.
• To introduce a spatial displacement parameter analogous to time lag.
• To extend spatial autocorrelation modeling for deeper geographical insights.

Main Methods:

• Development of 2D spatial autocorrelation functions based on Moran's index.
• Utilizing a relative staircase function for spatial weight matrix generation.
• Derivation of partial spatial autocorrelation functions via Yule-Walker equations.
• Generalization to functions based on Geary's coefficient and Getis' index.

Main Results:

• Successful construction of two types of 2D spatial autocorrelation functions.
• Demonstration of the framework's effectiveness in modeling spatial autocorrelation of Chinese cities.
• Validation of the relative step function as an effective basis for autocorrelation functions.

Conclusions:

• The developed spatial autocorrelation functions provide an effective analytical method.
• This framework enhances the understanding of deep geographical information and spatial dynamics.
• It lays a foundation for advanced spatial correlation and scaling analyses.