obtain_autocov_eigenvalues {fdaACF}

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}/\lambda_{1} > \code{epsilon} will be returned. By default epsilon = 0.0001.

Value

A vector containing the k eigenvalues greater than epsilon.

Examples

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)