Non-Stationary Semivariogram Analysis Using Real Estate Transaction Data

Geostatistical model is one of spatial statistical methodologies used for correcting spatial autocorrelation problem. To apply this model, two common assumptions should be made to allow global homogeneity: spatial continuity and spatial stationary. In different fields of research such as geography, environmental science and computer science, they usually take into account a violation of the second assumption (spatial stationary) but no article works under non-stationary condition in real estate research fields. This article is probably a first attempt to examine the violation of stationary assumption, in term of time and space, using transaction prices, from 1998 to 2007, of Parisian properties situated 5 kilometers around Arc de Triomphe. By comparing estimated 1-year semivariogram to 10-years semivariogram function, we found evidence of non-time-stationary. Likewise, non-spatial-stationary problem was detected by segmenting data in 90 degrees rotating windows. Our results show that we should not compute a common variogram for all parts of the region of interest.