RandomFields (version 3.0.10)

RMfractdiff: Fractionally Differenced Process Model

Description

RMfractdiff is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given for integers $r \in {\bf N}$ by $$C(r)=(-1{)}^r\frac{\mathrm{\Gamma }(1-a/2{)}^2}{\mathrm{\Gamma }(1-a/2+r)\mathrm{\Gamma }(1-a/2-r)}r\in \mathbf{N}$$ and otherwise linearly interpolated. Here $a \in [-1,1)$, $\Gamma$ denotes the gamma function. It can only be used for one-dimensional random fields.

Usage

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

Arguments

a

$-1 \le a < 1$

var,scale,Aniso,proj

optional parameters; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• RMfractdiff returns an object of class RMmodel.

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.

See Also

RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0)
model <- RMfractdiff(0.5, scale=0.2)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
RFoptions(seed=NA)