multiwave (version 1.0)

mww_eval: evaluation of multivariate wavelet Whittle estimation

Description

Evaluates the multivariate wavelet Whittle criterion at a given long-memory parameter vector d using DWTexact for the wavelet decomposition.

Usage

mww_eval(d, x, filter, LU = NULL)

Arguments

d

vector of long-memory parameters (dimension should match dimension of x).

x

data (matrix with time in rows and variables in columns).

filter

wavelet filter as obtain with scaling_filter.

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.)

Value

multivariate wavelet Whittle criterion.

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.

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 (2014) Multivariate wavelet Whittle estimation in long-range dependence. arXiv, http://arxiv.org/abs/1412.0391

See Also

mww, mww_cov_eval,mww_wav,mww_wav_eval,mww_wav_cov_eval

Examples

### 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 <- varfima(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)

res_mww <- mww_eval(d,x,filter,LU)
k <- length(d)
res_d <- optim(rep(0,k),mww_eval,x=x,filter=filter,
	  	        LU=LU,method='Nelder-Mead',lower=-Inf,upper=Inf)$par