K_eval: Evaluation of function K
In multiwave: Estimation of Multivariate Long-Memory Models Parameters

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1	K_eval(psi_hat,u,d)

`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.

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.

value of function K as a matrix.

S. Achard and I. Gannaz

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.

psi_hat_exact

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))