Given the coordinates in the Karhunen-Loève expansion
base of the Wiener, compute the coordinates in the
canonical basis.
Usage
BaseK2BaseC(x, nb)
Value
A object of class fdata with nb discretization points
and the same number of observations as x.
Arguments
x
A matrix containing the coordinates in the Karhunen-Loève basis.
One observation per column.
nb
The dimension of the canonical basis consider. By default,
the dimension is the same as the Karhunen-Loève one
(i.e. number of row of x).
Author
J. Damon
Details
The Karhunen-Loève expansion is a sum of an infinity of terms, but here
the expansion is truncated to a finite number of terms. Empirically, we
remark that using twice the dimension of the canonical basis desired
for the number of terms in the expansion is a good compromise.
References
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.