R: Fractionally Differenced Process Model

RMfractdiff {RandomFields} | R Documentation

## Fractionally Differenced Process Model

### Description

`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.

### Usage

    RMfractdiff(a, var, scale, Aniso, proj)

### Arguments

`a` | -1 ≤ a < 1
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

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.

### Value

`RMfractdiff` returns an object of class `RMmodel`.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### See Also

`RMmodel`, `RFsimulate`, `RFfit`.

### Examples

    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))

[Package RandomFields version 3.1.50 Index]