simul.far.wiener | R Documentation |
Simulation of a FAR(1) process using a Wiener noise.
simul.far.wiener(m=64, n=128, d.rho=diag(c(0.45, 0.9, 0.34, 0.45)), cst1=0.05, m2=NULL)
m |
Integer. Number of discretization points. |
n |
Integer. Number of observations. |
d.rho |
Numerical matrix. Expression of the first bloc of the linear operator in the Karhunen-Loève basis. |
cst1 |
Numeric. Perturbation coefficient on the linear operator. |
m2 |
Integer. Length of the Karhunen-Loève expansion (2 |
This function simulate a FAR(1) process with a Wiener noise. As for
the simul.wiener
, the function use the Karhunen-Loève
expansion of the noise. The FAR(1) process, defined by its linear
operator (see far
for more details), is computed in the
Karhunen-Loève basis then projected in the natural basis. The
parameters given in input (d.rho
and cst1
) are expressed
in the Karhunen-Loève basis.
The linear operator, expressed in the Karhunen-Loève basis, is of the form:
\code{d.rho} 0 \cr 0 eps.rho
Where d.rho
is the matrix provided in ths call, the two 0 are
in fact two blocks of 0, and eps.rho is a diagonal matrix having on
his diagonal the terms:
(eps(k+1), eps(k+2), …, eps(\code{m2}))
where
eps(i)= \code{cst1}/(i^2)+(1-\code{cst1})/exp(i)
and k is the length of the d.rho
diagonal.
The d.rho
matrix can be viewed as the information and the
eps.rho matrix as a perturbation. In this logic, the norm of eps.rho
need to be smaller than the one of d.rho
.
A fdata
object containing one variable ("var") which is a
FAR(1) process of length n
with m
discretization
points.
J. Damon
Pumo, B. (1992). Estimation et Prévision de Processus Autoregressifs Fonctionnels. Applications aux Processus à Temps Continu. PhD Thesis, University Paris 6, Pierre et Marie Curie.
fdata
, far
,
simul.far.wiener
.
far1 <- simul.far.wiener(m=64,n=100) summary(far1) print(far(far1,kn=4)) par(mfrow=c(2,1)) plot(far1,date=1) plot(select.fdata(far1,date=1:5),whole=TRUE,separator=TRUE)
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