论文标题
基于Moran指数的空间自相关函数的分析过程
An Analytical Process of Spatial Autocorrelation Functions Based on Moran's Index
论文作者
论文摘要
许多空间统计测量值，例如Moran的I和Geary的C，可用于空间自相关分析。空间自相关建模是从时间序列分析的一维自相关进行的，时间滞后被空间重量取代，因此自相关功能退化为自相关系数。本文使用相对楼梯函数作为重量函数，基于MORAN指数开发二维空间自相关函数，以产生带位移参数的空间重量矩阵。位移与时间序列分析的时间滞后相比。基于空间位移参数，构建了两种类型的空间自相关函数，用于二维空间分析。然后，部分空间自相关函数是通过Yule-Walker递归方程得出的。基于Geary的系数和GETIS索引，空间自相关函数被推广到自相关功能。例如，新的分析框架应用于中国城市的空间自相关建模。可以得出结论，是一种基于相对步骤函数构建自相关函数的有效方法。可以使用空间自相关函数来揭示深层的地理信息并执行空间动态分析，并为空间相关性的扩展分析奠定基础。
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 time lag of 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 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.
