K_eval function

Evaluation of function KK

Evaluation of function KK

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

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.

Details

K_eval computes the matrix KK with elements

K(dl,dm)=∫u(dl+dm)∣\codepsi_\codehat(u)∣2duK(dl,dm)=∫u(dl+dm)∗∣\codepsi_\codehat(u)∣2du. K(d_l,d_m)=\int u^{(d_l+d_m)} |\code{psi}\_\code{hat}(u)|^2 duK(d_l,d_m)=\int u^(d_l+d_m)*|\code{psi}\_\code{hat}(u)|^2 du.

Returns

value of function K as a matrix.

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.

Author(s)

S. Achard and I. Gannaz

See Also

psi_hat_exact

Examples

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))
multiwave packageRead PDF manual
  • Maintainer: Sophie Achard
  • License: GPL (>= 2)
  • Last published: 2019-05-06

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