obtain_autocov_eigenvalues: Estimate eigenvalues of the autocovariance function
Description
Estimate the eigenvalues of the sample autocovariance
function \(\hat{C}_{0}\). This functions returns the
eigenvalues which are greater than the value epsilon.
Usage
obtain_autocov_eigenvalues(v, Y, epsilon = 1e-04)
Arguments
v
Discretization points of the curves, by default
seq(from = 0, to = 1, length.out = 100).
Y
Matrix containing the discretized values
of the functional time series. The dimension of the
matrix is \((n x m)\), where \(n\) is the
number of curves and \(m\) is the number of points
observed in each curve.
epsilon
Value used to determine how many
eigenvalues will be returned. The eigenvalues
\(\lambda_{j} > \code{epsilon}\) will be returned.
By default epsilon = 0.0001.
Value
A vector containing the \(k\) eigenvalues
greater than epsilon.
# NOT RUN {N <- 100
v <- seq(from = 0, to = 1, length.out = 10)
sig <- 2
Y <- simulate_iid_brownian_bridge(N, v, sig)
lambda <- obtain_autocov_eigenvalues(v = v, Y = Y)
# }