A spatio-temporal measure of spatial dependence : an example using real estate data

The computation of Moran's I index and his statistics test relies mainly on an exogenous specification of a spatial weights matrix. However, the exogenous weights matrix is usually developed in a strictly spatial context, even when data are collected over time. This paper develops a spatio-temporal weights matrix and uses the new definition to evaluate spatial dependence using Moran's I index applied to real estate data for Quebec City from 1986 to 1996. The results are compared with the original Moran's I index using a strictly spatial weights matrix specification based on Euclidian distance or contiguity. The findings suggest that ignoring the temporal dimension could lead to misinterpretation of the ‘real’ measure of spatial dependence over time. However, the time dimension cannot explain the total spatial autocorrelation since the Moran's I index is still significant even when adjusting for time consideration. The differences between the estimated indices and statistics depend on the structure of the spatial and the temporal weights matrices that are used to construct the complete spatio-temporal weights matrix