scaling_function {multiwave}

scaling function and the wavelet function

Description

Computes the scaling function and the wavelet function (for compactly supported wavelet) using the cascade algorithm on the grid of dyadic integer 2^{-J}

Usage

scaling_function(filter,J)

Arguments

filter

wavelet filter as obtained with scaling_filter.

J

value of the largest scale.

Value

phi

Scaling function.

psi

Wavelet function.

Note

This function was rewritten from an original matlab version by Fay et al. (2009)

Author(s)

S. Achard and I. Gannaz

References

G. Fay, E. Moulines, F. Roueff, M. S. Taqqu (2009) Estimators of long-memory: Fourier versus wavelets. Journal of Econometrics, vol. 151, N. 2, pages 159-177.

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

DWTexact, scaling_filter

Examples

res_filter <- scaling_filter('Daubechies',8);
filter <- res_filter$h
scaling_function(filter,J=6)