# Sample a Multivariate Locally Stationary Wavelet Process Sample a multivariate locally stationary wavelet process. methods ```r rmvLSW(Transfer = NULL, Spectrum = NULL, noiseFN = rnorm, ...) ## S3 method for class 'mvLSW' simulate(object, nsim = 1, seed = NULL, ...) ``` ## Arguments - `Transfer`: A `mvLSW` object containing the set of transfer function matrices of the process. - `Spectrum, object`: A `mvLSW` object containing the multivariate evolutionary wavelet spectrum of the process. This argument is only used if `Transfer` is not supplied. - `noiseFN`: The function for sampling the innovations. - `nsim`: Number of mvLSW time series to draw. Only `nsim = 1` is accepted. - `seed`: Seed for the random number generator. - `...`: Optional arguments to be passed to the function for sampling the innovation process. ## Details Samples a single multivariate locally stationary wavelet time series for the given set of transfer function matrices. These are assumed to be lower-triangular (including diagonal) matrices. If the mvEWS is supplied instead, then this is pre-processed by `Spectrum2Transfer()` to obtain the transfer function matrices. The `Transfer` and `Spectrum` are both `mvLSW` objects and therefore contain information about defining the wavelet function. The innovation process is assumed to be second order stationary with expectation zero, orthogonal and unit variance. The first argument of `noiseFN` must be `n` and define the number of samples to generate. The function must also return a numerical vector of length `n`. The `simulate` command implements `rmvLSW` under default arguments unless specified via `...`. ## Returns A `ts` matrix object of a multivariate locally stationary time series. The columns of the matrix correspond to different channels and the rows identify the time axis. ## References Taylor, S.A.C., Park, T.A. and Eckley, I. (2019) Multivariate locally stationary wavelet analysis with the mvLSW R package. **Journal of statistical software** 90 (11) pp. 1--16, doi: 10.18637/jss.v090.i11. Park, T., Eckley, I. and Ombao, H.C. (2014) Estimating time-evolving partial coherence between signals via multivariate locally stationary wavelet processes. **Signal Processing, IEEE Transactions on** 62 (20) pp. 5240-5250. ## See Also `mvLSW`, `Spectrum2Transfer`, `rnorm`, `AvBasis`, `ts`. ## Examples ```r ## Define evolutionary wavelet spectrum, structure only on level 2 Spec <- array(0, dim = c(3, 3, 8, 256)) Spec[1, 1, 2, ] <- 10 Spec[2, 2, 2, ] <- c(rep(5, 64), rep(0.6, 64), rep(5, 128)) Spec[3, 3, 2, ] <- c(rep(2, 128), rep(8, 128)) Spec[2, 1, 2, ] <- Spec[1, 2, 2, ] <- punif(1:256, 65, 192) Spec[3, 1, 2, ] <- Spec[1, 3, 2, ] <- c(rep(-1, 128), rep(5, 128)) Spec[3, 2, 2, ] <- Spec[2, 3, 2, ] <- -0.5 ## Define Haar wavelet function and create mvLSW object EWS <- as.mvLSW(x = Spec, filter.number = 1, family = "DaubExPhase", min.eig.val = NA) plot(EWS, style = 2, info = 2) ## Sample with Gaussian innovations set.seed(10) X <- rmvLSW(Spectrum = EWS) plot(X) ## Alternatively: X1 <- simulate(object = EWS) plot(X1) ## Define smoother wavelet function and create mvLSW object EWS2 <- as.mvLSW(x = Spec, filter.number = 10, family = "DaubExPhase") ## Sample with logistic innovations set.seed(10) X2 <- rmvLSW(Spectrum = EWS2, noiseFN = rlogis, scale = sqrt(3)/pi) plot(X2) ```

rmvLSW function