Adaptive wavelet-based bootstrapping

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Description

Given a set of indices which represent the whitest transform available in a DWPT, this function randomizes the coefficients in each of the crystals comprising the transform (via random selection with replacement) followed by an inverse transform. The z is a bootstrapped version of the original time series.

Usage

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wavBootstrap(x, white.indices=wavDWPTWhitest(x),
    n.realization=1, wavelet="s8", n.level=NULL)

Arguments

x

a vector containing a uniformly-sampled real-valued time series or an object of class wavTransform as output by the wavDWPT function.

n.level

the number of decomposition levels. This argument is used only if x is a time series. Default: floor(logb(length(x), base=2)) - 2.

n.realization

the number of realizations to generate. Default: 1.

wavelet

a character string denoting the filter type. See wavDaubechies for details. This argument is used only if x is a time series. Default: "s8".

white.indices

a list containing the level and osc vectors denoting the level and oscillation index, respectively, of the whitest transform. Default: wavDWPTWhitest(x).

Value

a list of numeric vectors containing the bootstrapped series. If n.realization=1, the the output is a numeric vector (not packed into a list).

References

D. B. Percival, S. Sardy and A. C. Davison, Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping, in W. J. Fitzgerald, R. L. Smith, A. T. Walden and P. C. Young (Eds.), Nonlinear and Nonstationary Signal Processing, Cambridge, England: Cambridge University Press, 2001.

See Also

wavDWPT, wavDWPTWhitest.

Examples

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## wavestrap the sunspots series 
x <- as.numeric(sunspots)
z <- wavBootstrap(x, n.realization=1)

stackPlot(x=seq(along=sunspots),
y=data.frame(x, z, abs(z)),
ylab=list(text=c("sunspots","wavestrap","|wavestrap|")))

title("Wavelet-based bootstrapping of sunspots series", cex=0.7)

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