R: Single temporal process

RMstp {RandomFields} | R Documentation

## Single temporal process

### Description

`RMstp` is a univariate covariance model which depends on a normal mixture submodel phi. The covariance is given by

C(x,y) = |S_x|^{1/4} |S_y|^{1/4} |A|^{-1/2} φ(Q(x,y)^{1/2})

where

Q(x,y) = c^2 - m^2 + h^t (S_x + 2(m + c)M) A^{-1} (S_y + 2 (m-c)M)h,

c = -z^t h + ξ_2(x) - ξ_2(y),

A = S_x + S_y + 4 M h h^t M

m = h^t M h

h = x - y

### Usage

    RMstp(xi, phi, S, z, M, var, scale, Aniso, proj)

### Arguments

`xi` | arbitrary univariate function on R^d
`phi` | an `RMmodel` that is a normal mixture model, cf. `RFgetModelNames(monotone="normal mixture")`
`S` | functions that returns strictly positive definite d x d
`z` | arbitrary vector, z \in R^d
`M` | an arbitrary, symmetric d x d matrix
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

See Schlather (2008) formula (13). The model allows for mimicking cyclonic behaviour.

### Value

`RMstp` returns an object of class `RMmodel`

### Author(s)

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

### References

- Paciorek C.J., and Schervish, M.J. (2006) Spatial modelling using a new class of nonstationary covariance functions, Environmetrics 17, 483-506.

- Schlather, M. (2010) Some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.

### 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 <- RMstp(xi = RMrotat(phi= -2 * pi, speed=1),
                   phi = RMwhittle(nu = 1),
                   M=matrix(nc=3, rep(0, 9)),
                   S=RMetaxxa(E=rep(1, 3), alpha = -2 * pi,
                              A=t(matrix(nc=3, c(2, 0, 0, 1, 1 , 0, 0, 0, 0))))
                  )
    x <- seq(0, 10, 0.7)
    plot(RFsimulate(model, x=x, y=x, z=x))

[Package RandomFields version 3.1.50 Index]