THE CORRELATION STRUCTURE OF SPATIAL AUTOREGRESSIONS
研究一阶同时自回归模型中权重矩阵和自回归参数如何影响空间单元间的相关性，利用图论中的路径表示解释相关性质，并比较有向与无向网络的差异。
This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties of W to correlation properties of SAR(1) models defined on irregular lattices.