Spatial Autocorrelation Function of a Process in the Plane

It computes the autocorrelation function of a process in the plane z=g(x,y), with coordinates x,y, sampled at random points {Xi,Yi;Zi}.

This program computes Spatial Autocorrelation functions (SACRF) of a stochastic process in the plane z=g(x,y), where x,y are planar coordinates (e.g. longitude and latitude), given N data {Xi,Yi;Zi} points. The serial correlation is defined as Rk=Corr(Zi,Zi-k), where Zi-k is k-th nearest neighbor (NN) of the data Zi, according to the Euclidean distance Dik=sqrt((Xi-Xi-k)^2+(Yi-Yi-k)^2). The SACRF is also be computed with respect to the k-th North NN (to satify a principle of causal spatial ordering), and using the inverse distances 1/Dik as weights for the products Zi*Zi-k (IDW principle). Finally the SACRF is computed with respect to averages of the points Zi-k which fall in the k-th ring around Zi.