Simone,
My understanding of Intrinsic Hypothesis is that it is based on the stationarity of both difference (1st order) and variance of difference (2nd order). So the statement your wrote " Intrinsic hypothesis is different from second order one mainly because in the first case covariance function does not exist and variogram is computed instead of it...." does not make sense to me. >The problem is how to realize about the intrinsicness of my variable...what >does "covariance does not exist" mean?...I can calculate covariance with ISATIS >and when variogram increases not bounding around a priori variance my >covariance will be negative...but it continue to exist!....so how to >distinguish second order from intrinsic variables?....and decide if beeing able >to use only variogram or choose between covariance or variogram?.... There is a trick in the relationship between "stationarity" and "existing of variogram". Here is my logic, (1) When there is stationarity of both 1st and 2nd order, the semivariogram exists. On the other hand, (2) If there is semivariogrm exists, does that mean the stationarity of both 1st and 2nd order exist? Intrinsicness Theory is based on ideal situation I can not totally agree after some simulation I have done. The first case prevails, but not the second case. When you have second order, or covariance, non-stationarity, it does not mean the covariance not exising. Rather, it means the variation is too large and the 2nd order stationarity does not exist. The 2nd order stationarity is also called homoskedasticity, while non-stationarity is heteroskedasticity (Check out http://www.riskglossary.com/articles/heteroskedasticity.htm) There are two ways we can salvage 2nd order non-stationarity in my opinion: First is about scale. If the study area is large and contains many data, instead of using the whole area, conduct some cluster analysis and break the area into smaller scale areas, each of which may abide by intrinsic hypothesis. This means you will get semivariograms on each sub-region of the whole study area. Second way is about transforamtion. If the data is limited or the study area is small, conduct some standardized transformation of data so the covariance will become stationary. Hope this helps. Shing Shing-Tzong Lin Teaching and Research Assistant Department of Geography Texas State University, San Marcos (512)245-1935
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