# Multivariate Locally Stationary Wavelet Object Constructs a multivariate locally stationary wavelet (mvLSW) object. methods ```r as.mvLSW(x, filter.number = 1, family = "DaubExPhase", smooth.type = "all", smooth.kernel = kernel("daniell", 0), bias.correct = FALSE, min.eig.val = -Inf, names = NULL) is.mvLSW(object) ``` ## Arguments - `x`: 4D array of order PxPxJxT where P is the number of channels of the time series of length T such that T=$2^J$ for some positive integer J defining the levels of the mvLSW object. - `family`: Character string specifying the wavelet family. Only two options are available, either `"DaubExPhase"` (default) or `"DaubLeAsymm"`. - `filter.number`: Integer number defining the number of vanishing moments of the wavelet function. By default, `filter.number=1` and so defining the Haar wavelet. - `smooth.type`: What type of smoothing regime has been applied. Either `"all"` (default) if the smoothing method been applied to all levels. Otherwise `"by.level"`, a different smoothing method is applied to each level. - `smooth.kernel`: Definition of the smoothing kernel from `kernel()`. By default, the identity kernel is defined. - `bias.correct`: Logical, has a bias correction been applied to the data. `FALSE` by default. - `min.eig.val`: Minimum eigenvalue from spectral matrices across all levels and locations, set at `-Inf` by default. If `NA`, then the minimum eigenvalue is calculated. - `names`: Character vector containing the channel names of the multivariate time series. - `object`: Any R object. ## Details `as.mvLSW` constructs a multivariate locally stationary classed object that contains all information about the constructions of various multivariate wavelet estimates. The command `is.mvLSW` checks that the supplied R object is a valid `mvLSW` object in that its structure and contents are as expected. ## Returns The `as.mvLSW` command invisibly returns a list with the following items: - **spectrum**: A 4D array containing the data relating to the estimate of interest. - **Information**: List containing information on the estimation procedure. The list `Information` contains: - **names**: Character vector containing the channel names. - **dimensions**: A list containing items `P` - the number of channels forming of the time series, `T` - the length of the time series and `J` - the number of levels in the wavelet transform of the data. - **wavelet**: A list containing the `filter.number` and `family` of the wavelet used in the transformation. - **smooth**: A list detailing applied smoothing of the estimate. Items include: `smooth.type` - name of the smoothing regime. `smooth.kernels` - a `tskernel` class from the command `kernel()`. `GCV` - generalized cross-validation gamma deviance criterion of the smoothing. `smooth.eps` - smoothing threshold. If `smooth.type="by.level"`, then `smooth.kernels` is a list containing the `tskernel` object for each level from fine to coarse. In addition, `GCV` is a length J vector containing the criterion estimate for each level from fine to coarse. - **correction**: A list containing `bias.correction` and `min.eig.val`. The command `is.mvLSW` returns `TRUE` if the supplied object is a valid `mvLSW` object as described above. Otherwise, the command returns `FALSE`. ## 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. ## See Also `mvEWS`, `varEWS`, `kernel`. ## 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 EWS as mvLSW object EWS <- as.mvLSW(x = Spec, filter.number = 1, family = "DaubExPhase", names = c("A", "B", "C"), min.eig.val = NA) is.mvLSW(EWS) plot(EWS, style = 2, info = 2) ```

as.mvLSW function