multiwave (version 1.4)

K_eval: Evaluation of function \(K\)

Description

Computes the function \(K\) as defined in (Achard and Gannaz 2014).

Usage

K_eval(psi_hat,u,d)

Arguments

psi_hat

Fourier transform of the wavelet mother at values u

u

grid for the approximation of the integral

d

vector of long-memory parameters.

Value

value of function K as a matrix.

Details

K_eval computes the matrix \(K\) with elements

$$K(d_l,d_m)=\int u^{(d_l+d_m)} |\code{psi}\_\code{hat}(u)|^2 du $$

References

S. Achard, I. Gannaz (2016) Multivariate wavelet Whittle estimation in long-range dependence. Journal of Time Series Analysis, Vol 37, N. 4, pages 476-512. http://arxiv.org/abs/1412.0391.

S. Achard, I Gannaz (2019) Wavelet-Based and Fourier-Based Multivariate Whittle Estimation: multiwave. Journal of Statistical Software, Vol 89, N. 6, pages 1-31.

See Also

psi_hat_exact

Examples

# NOT RUN {
res_filter <- scaling_filter('Daubechies',8);
filter <- res_filter$h
M <- res_filter$M
alpha <- res_filter$alpha
res_psi <- psi_hat_exact(filter,J=10)
K_eval(res_psi$psih,res_psi$grid,d=c(0.2,0.2))
# }