# mww_wav_eval: multivariate wavelet Whittle estimation for data as wavelet... In multiwave: Estimation of Multivariate Long-Memory Models Parameters

## Description

Evaluates the multivariate wavelet Whittle criterion at a given long-memory parameter vector d for the already wavelet decomposed data.

## Usage

 1 mww_wav_eval(d, xwav, index, LU = NULL) 

## Arguments

 d vector of long-memory parameters (dimension should match dimension of x). xwav wavelet coefficients matrix (with scales in rows and variables in columns). index 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)]. LU bivariate vector (optional) containing L, the lowest resolution in wavelet decomposition U, the maximal resolution in wavelet decomposition. (Default values are set to L=1, and U=Jmax.)

## Details

L is fixing the lower limit of wavelet scales. L can be increased to avoid finest frequencies that can be corrupted by the presence of high frequency phenomena.

U is fixing the upper limit of wavelet scales. U can be decreased when highest frequencies have to be discarded.

## Value

multivariate wavelet Whittle criterion.

## Author(s)

S. Achard and I. Gannaz

## References

E. Moulines, F. Roueff, M. S. Taqqu (2009) A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series. Annals of statistics, vol. 36, N. 4, pages 1925-1956

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.

mww, mww_cov_eval,mww_wav,mww_eval,mww_wav_cov_eval

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 ### Simulation of ARFIMA(0,d,0) rho <- 0.4 cov <- matrix(c(1,rho,rho,1),2,2) d <- c(0.4,0.2) J <- 9 N <- 2^J resp <- fivarma(N, d, cov_matrix=cov) x <- resp$x long_run_cov <- resp$long_run_cov ## wavelet coefficients definition res_filter <- scaling_filter('Daubechies',8); filter <- res_filter$h LU <- c(2,11) ### wavelet decomposition if(is.matrix(x)){ N <- dim(x)[1] k <- dim(x)[2] }else{ N <- length(x) k <- 1 } x <- as.matrix(x,dim=c(N,k)) ## Wavelet decomposition xwav <- matrix(0,N,k) for(j in 1:k){ xx <- x[,j] resw <- DWTexact(xx,filter) xwav_temp <- resw$dwt index <- resw$indmaxband Jmax <- resw$Jmax xwav[1:index[Jmax],j] <- xwav_temp; } ## we free some memory new_xwav <- matrix(0,min(index[Jmax],N),k) if(index[Jmax]

### Example output


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multiwave documentation built on May 6, 2019, 9:02 a.m.