rmvLSW {mvLSW}

Sample a Multivariate Locally Stationary Wavelet Process

Description

Sample a multivariate locally stationary wavelet process.

Usage

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 ....

Value

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

## 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)