mvLSW (version 1.0)

rmvLSW: Sample a Multivariate Locally Stationary Wavelet Process

Description

Sample a Multivariate Locally Stationary Wavelet Process.

Usage

rmvLSW(Transfer = NULL, Spectrum = NULL, noiseFN = rnorm, ...)

Arguments

Transfer

A mvLSW object containing the set of transfer function matrices of the process.

Spectrum

A mvLSW object containing the evolutionary wavelet spectrum of the process. This argument is only used if Transfer is not supplied.

noiseFN

The function for sampling the innovations.

...

Optional arguments to be passed to noiseFN.

Value

A ts matrix object of a locally stationary time series. The columns of the matrix correspond to different signals and the rows identify the time location.

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 evolutionary wavelet spectrum 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.

References

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

## 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, ] <- c(rep(0, 64), seq(0, 1, len=128), rep(1, 64))
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 <- mvLSW(spectrum = 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)

## Define smoother wavelet function and create mvLSW object
EWS2 <- mvLSW(spectrum = Spec, filter.number = 10, family = "DaubExPhase")

## Sample with logisitc innovations
set.seed(10)
X2 <- rmvLSW(Spectrum = EWS2, noiseFN = rlogis, scale = sqrt(3)/pi)
plot(X2)