Space-time moving average model
RMave is a univariate stationary covariance model
which depends on a normal scale mixture covariance model phi.
The corresponding covariance function only depends on the difference between two points in the d-dimensional space and is given by
C(h, u) = |E + 2 A h h^t A|^{-1/2} phi(sqrt[|h|^2/2 + (z^t h + u)^2 (1 - 2h^t A (E + 2 A h h^t A)^{-1} A h)])
where E is the identity matrix. The spatial dimension is d-1 and h is real-valued.
RMave(phi, A, z, spacetime, var, scale, Aniso, proj)
phi |
a covariance model which is a normal mixture, that means an
|
A |
a symmetric d-1 x d-1-matrix if the corresponding random field is in the d-dimensional space |
z |
a d-1 dimensional vector if the corresponding random field is on d-dimensional space |
spacetime |
logical. If FALSE then the model is interpreted as
if h=0, i.e. the spatial dimension is d. Default is |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
See Schlather, M. (2010), Example 13 with l=1.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Schlather, M. (2010) Some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.
RFfit,
RFsimulate,
RMmodel,
RMstp.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
## Example of an evaluation of the ave2-covariance function
## in three different ways
## ---------------------------------------------------------
## some parameters A and z
A <- matrix(c(2,1,1,2),ncol=2)
z <- c(1,2)
## h for evalutation
h <- c(1,2)
## some abbreviations
E <- matrix(c(1,0,0,1),ncol=2)
B <- A %*% h %*% t(h) %*% A
phi <- function(t){return(RFcov(RMwhittle(1), t))}
## ---------------------------------------------------------
## the following should yield the same value 3 times
## (also for other choices of A,z and h)
z1 <- RFcov( model=RMave(RMwhittle(1),A=A,z=z) , x=t(c(h,0)) )
z2 <- RFcov( model=RMave(RMwhittle(1),A=A,z=z,spacetime=FALSE) , x=t(h) )
z3 <- ( (det(E+2*B))^(-1/2) ) *
phi( sqrt( sum(h*h)/2 + (t(z) %*% h)^2 *
( 1-2*t(h) %*% A %*% solve(E+2*B) %*% A %*% h) ) )
##
## Not run: stopifnot(abs(z1-z2)<1e-12, abs(z2-z3)<1e-12)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.