DWTexact: Exact discrete wavelet decomposition

Description

Computes the discrete wavelet transform of the data using the pyramidal algorithm.

Usage

DWTexact(x, filter)

Arguments

vector of raw data

filter

Quadrature mirror filter (also called scaling filter, as returned by the scaling_filter function)

Value

dwt

computable Wavelet coefficients without taking into account the border effect.

indmaxband

vector containing the largest index of each band, i.e. for \(j > 1\) the wavelet coefficients of scale \(j\) are \(\code{dwt}(k)\) for \(k \in [\code{indmaxband}(j-1)+1,\code{indmaxband}(j)]\) and for \(j=1\), \(\code{dwt}(k)\) for \(k \in [1,\code{indmaxband}(1)]\).

Jmax

largest available scale index (=length of indmaxband).

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.

Examples

Run this code

# NOT RUN {
res_filter <- scaling_filter('Daubechies',8);
filter <- res_filter$h
u <- rnorm(2^10,0,1)
x <- vfracdiff(u,d=0.2)

	resw <- DWTexact(x,filter)
		xwav <- resw$dwt
		index <- resw$indmaxband
		Jmax <- resw$Jmax

## Wavelet scale 1
ws_1 <- xwav[1:index[1]]
## Wavelet scale 2
ws_2 <- xwav[(index[1]+1):index[2]]
## Wavelet scale 3
ws_3 <- xwav[(index[2]+1):index[3]]
### upto Jmax



# }