I have some problems in understanding the usage of argument 'stAni' of vgmST and krigeST functions, for the setting of spatio temporal anisotropy.

How have I to interpret this argument, that is the integer value that I saw I have to assign to it, what does it mean?

How can this argument influence the result of prediction? 

Are units of spatial and temporal ranges and lags related to this argument?

How can I study the spatio temporal anisotropy of my data?

1 Answer 1

   stAni: A spatio-temporal anisotropy; the number of space units
          equivalent to one time unit.

and it is only used in spatio-temporal variograms that have a metric to them. By this it is meant that you can compute a distance between two points S at (x,y,t) and S' at (x',y',t').

For the "separable" variograms, the semi-variance is a product of a spatial and a temporal component: Y(S, S') = s((x,y),(x',y')).t(t,t'). There's no real concept of a single-measure "distance" between S and S' - suppose they are 6km apart and two days apart. Are they closer or further apart than two points 4km apart and three days apart? That often doesn't make sense, and a separable space-time variogram avoids this question by assuming the variance depends independently on the spatial distance and the temporal distance.

The "metric" variograms are different. The stAni parameter says how many space units are equivalent to a time unit - and in this way define a speed.

So a point at (0,0,0) is five spatial units from a point at (3,4,0), and if stAni is 1, it is at the same distance from a point (0,0,5) - ie in the same location but but five days later. In a metric variogram those pairs of points will have the same variance.

If you want to explore space-time anisotropy in data then you should probably plot a space-time variogram and see what that tells you.

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