# evaluation of multivariate wavelet Whittle estimation Evaluates the multivariate wavelet Whittle criterion at a given long-memory parameter vector `d` using `DWTexact` for the wavelet decomposition. ```r 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`.) ## 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. ## Returns multivariate wavelet Whittle criterion. ## 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. ## Author(s) S. Achard and I. Gannaz ## See Also `mww`, `mww_cov_eval`,`mww_wav`,`mww_wav_eval`,`mww_wav_cov_eval` ## Examples ```r ### 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$alpha LU <- c(2,11) res_mww <- mww_eval(d,x,filter,LU) k <- length(d) res_d <- optim(rep(0,k),mww_eval,x=x,filter=filter, LU=LU,method='Nelder-Mead',lower=-Inf,upper=Inf)$par ```

mww_eval function