Description Usage Arguments Value Note Author(s) References See Also Examples
Computes the discrete wavelet transform of the data using the pyramidal algorithm.
1 |
x |
vector of raw data |
filter |
Quadrature mirror filter (also called scaling filter, as returned by the |
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 |
This function was rewritten from an original matlab version by Fay et al. (2009)
S. Achard and I. Gannaz
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | 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
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