Fractionally Differenced Process Model
RMfractdiff is a stationary isotropic covariance model.
The corresponding covariance function only depends on the distance
r ≥ 0 between two points and is given for integers
r by
C(r) = (-1)^r Γ(1-a/2)^2 / (Γ(1-a/2+r) Γ(1-a/2-r))
and otherwise linearly interpolated. Here, -1 ≤ a < 1, Γ denotes the gamma function. It can only be used for one-dimensional random fields.
RMfractdiff(a, var, scale, Aniso, proj)
a |
-1 ≤ a < 1 |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
The model is only valid for dimension d = 1 . It stems from time series modelling where the grid locations are multiples of the scale parameter.
RMfractdiff returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMfractdiff(0.5, scale=0.2) x <- seq(0, 10, 0.02) plot(model) plot(RFsimulate(model, x=x))
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