# Estimation of multivariate long-memory models parameters: memory parameters and long-run covariance matrix (also called fractal connectivity). This package computes an estimation of the long-memory parameters and the long-run covariance matrix using a multivariate model (Lobato, 1999; Shimotsu 2007). Two semi-parametric methods are implemented: a Fourier based approach (Shimotsu 2007) and a wavelet based approach (Achard and Gannaz 2014). package ## Details ||| |:--|:--| |Package:|multiwave| |Type:|Package| |Version:|1.0| |Date:|2015-09-17| |License:|GPL (>= 2)| ## Author(s) Sophie Achard and Irene Gannaz Maintainer: Sophie Achard , Irene Gannaz ## References 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. ## Examples ```r 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 #### Compute wavelets this is also included in the functions without _wav res_filter <- scaling_filter('Daubechies',8); filter <- res_filter$h M <- res_filter$M alpha <- res_filter$alpha LU <- c(1,11) if(is.matrix(x)){ N <- dim(x)[1] k <- dim(x)[2] }else{ N <- length(x) k <- 1 } mat_x <- as.matrix(x,dim=c(N,k)) ## Wavelet decomposition xwav <- matrix(0,N,k) for(j in 1:k){ xx <- mat_x[,j] resw <- DWTexact(xx,filter) xwav_temp <- resw$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]

multiwave-package