at.wd {WASP}

a trous (AT) based additive decompostion using Daubechies family wavelet

Description

a trous (AT) based additive decompostion using Daubechies family wavelet

Usage

at.wd(x, wf, J, boundary = "periodic")

Arguments

x

The input time series.

wf

Name of the wavelet filter to use in the decomposition.

J

Specifies the depth of the decomposition. This must be a number less than or equal to log(length(x),2).

boundary

Character string specifying the boundary condition. If boundary=="periodic" the default, then the vector you decompose is assumed to be periodic on its defined interval, if boundary=="reflection", the vector beyond its boundaries is assumed to be a symmetric reflection of itself.

Value

A matrix of decomposed sub-time series.

References

Nason, G. P. (1996). Wavelet shrinkage using cross-validation. Journal of the Royal Statistical Society: Series B (Methodological), 58(2), 463-479.

Examples

data(obs.mon)

n <- nrow(obs.mon)
v <- 1
J <- floor(log(n / (2 * v - 1)) / log(2)) # (Kaiser, 1994)

names <- colnames(obs.mon)
at.atm <- vector("list", ncol(obs.mon))
for (i in seq_len(ncol(obs.mon))) {
  tmp <- as.numeric(scale(obs.mon[, i], scale = FALSE))
  at.atm <- do.call(cbind, at.wd(tmp, wf = "haar", J = J, boundary = "periodic"))

  plot.ts(cbind(obs.mon[1:n, i], at.atm[1:n, 1:9]), main = names[i])
  print(sum(abs(scale(obs.mon[1:n, i], scale = FALSE) - rowSums(at.atm[1:n, ]))))
}