Description Usage Arguments Details Value Author(s) References See Also Examples
Computes the multivariate wavelet Whittle estimation of the long-run covariance matrix given the long-memory parameter vector d
for the already wavelet decomposed data.
1 | mww_wav_cov_eval(d, xwav, index,psih,grid_K, LU)
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d |
vector of long-memory parameters (dimension should match dimension of xwav). |
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)]. |
psih |
the Fourier transform of the wavelet mother at values |
grid_K |
the grid for the approximation of the integral in K |
LU |
bivariate vector (optional) containing
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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.
Long-run covariance matrix estimation.
S. Achard and I. Gannaz
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_eval
,mww_wav
,mww_wav_eval
,mww_cov_eval
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 51 52 53 54 55 | ### 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$h
M <- res_filter$M
alpha <- res_filter$alpha
LU <- c(2,11)
### wavelet decomposition
if(is.matrix(x)){
N <- dim(x)[1]
k <- dim(x)[2]
}else{
N <- length(x)
k <- 1
}
x <- as.matrix(x,dim=c(N,k))
## Wavelet decomposition
xwav <- matrix(0,N,k)
for(j in 1:k){
xx <- x[,j]
resw <- DWTexact(xx,filter)
xwav_temp <- resw$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]<N){
new_xwav[(1:(index[Jmax])),] <- xwav[(1:(index[Jmax])),]
}
xwav <- new_xwav
index <- c(0,index)
##### Compute the wavelet functions
res_psi <- psi_hat_exact(filter,10)
psih<-res_psi$psih
grid<-res_psi$grid
res_mww <- mww_wav_cov_eval(d,xwav,index, psih, grid,LU)
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