Hope this email finds you well. I want to ask if there is a formal test for
spatial stationarity like the one for temporal stationarity. I have
searched a lot, but I could not find a formal test by which we can conclude
about stationarity in spatial data.
I would be grateful if anyone can help me with this.
> Dear all
> Hope this email finds you well. I want to ask if there is a formal test
> for spatial stationarity like the one for temporal stationarity. I have
> searched a lot, but I could not find a formal test by which we can
> conclude about stationarity in spatial data.
Could you please clarify what you mean by "spatial data"? Do you mean
point observations of a continuous spatial process - say to make
predictions for unobserved locations, as in kriging? In this case, there
is a formal literature discussing stationarity, although I'm not aware of
formal tests (practically one might compare predictions made using models
that assume stationarity and those that do not, to see whether the
assumption changes the output; if it does, probably stationarity is not
present as assumed).
In the point process literature (point patterns), there are also results,
but they are often handled by relaxing assumptions about the homogeneity
of the underlying surface (introducing covariates influencing the
For lattice (aggregated, polygon) data, there are tests based on
geographically weighted regression, but these lack power if the bandwidth
is inappropriate and/or the underlying model is mis-specified. They are
not univariate tests, and may best be seen as exploratory. There may be
other literatures, look for work for example by Werner Mueller and