mra: Multiresolution Analysis

In wavelets: Functions for Computing Wavelet Filters, Wavelet Transforms and Multiresolution Analyses

Description

Computes the multiresolution analysis for a univariate or multivariate time series.

Usage

mra(X, filter="la8", n.levels, boundary="periodic", fast=TRUE, method="dwt")

Arguments

X	A univariate or multivariate time series. Numeric vectors, matrices and data frames are also accepted.
filter	Either a wt.filter object, a character string indicating which wavelet filter to use in the decomposition, or a numeric vector of wavelet coefficients (not scaling coefficients). See help(wt.filter) for acceptable filter names.
n.levels	An integer specifying the level of the decomposition. By default this is the value J such that the length of X is at least as great as the length of the level J wavelet filter, but less than the length of the level J+1 wavelet filter. Thus, j <= log((N-1)/(L-1)+1), where N is the length of X.
boundary	A character string indicating which boundary method to use. boundary = "periodic" and boundary = "reflection" are the only supported methods at this time.
fast	A logical flag which, if true, indicates that the pyramid algorithm is computed with an internal C function. Otherwise, only R code is used in all computations.
method	A character string, taking values "dwt" or "modwt", that indicates which type of transform to use when computing the MRA.

Value

Returns an object of class mra, which is an S4 object with slots

D	A list with element i comprised of a matrix containing the ith level wavelet detail.
S	A list with element i comprised of a matrix containing the ith level wavelet smooths.
filter	A wt.filter object containing information for the filter used in the decomposition. See help(wt.filter) for details.
level	An integer value representing the level of wavelet decomposition.
boundary	A character string indicating the boundary method used in the wavelet decomposition. Valid values are "periodic" or "reflection".
series	The original time series, X, in matrix format.
class.X	A character string indicating the class of the input series. Possible values are "ts", "mts", "numeric", "matrix", or "data.frame".
attr.X	A list containing the attributes information of the original time series, X. This is useful if X is an object of class ts or mts and it is desired to retain relevant time information. If the original time series, X, is a matrix or has no attributes, then attr.X is an empty list.
method	A character string indicating which type of wavelet decomposition was performed (either "dwt" or "modwt").

Author(s)

Eric Aldrich. [e-mail].

References

Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

See Also

dwt, modwt, wt.filter.

Examples

# obtain the two series listed in Percival and Walden (2000), page 42
X1 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,.7,.9,0,.3)
X2 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,-.7,.9,0,.3)

# combine them and compute MRA
newX <- cbind(X1,X2)
mra.out <- mra(newX, n.levels=3, boundary="reflection")

Example output

wavelets documentation built on March 26, 2020, 6:50 p.m.