wmtsa (version 1.1-1)

wavDWPTWhitest: Seeks the whitest transform of a discrete wavelet packet transform (DWPT)

Description

This function seeks the whitest orthonormal transform of a DWPT. The goal is to segment the normalized frequency interval $f \in [0, 1/2]$ into subintervals such that, within each subinterval, the variability of the (corresponding) spectral density function (SDF) is minimized, i.e., each segment of the SDF is as flat as possible. Given an $N$-point uniformly sampled time series X, and denoting $\mathbf{W}_{j,n}$ as the DWPT crystal at level $j$ and (sequency ordered) oscillation index $n$, this optimization is achieved as follows:

[object Object],[object Object],[object Object]

Usage

wavDWPTWhitest(x, significance=0.05, test="port2", wavelet="s8", n.level=NULL)

Arguments

x

a vector containing a uniformly-sampled real-valued time series or an object of class wavTransform.

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.

significance

a numeric value on the interval (0,1) which qualitatively signifies the fraction of times that the white noise hypothesis is incorrectly rejected. The significance is used to calculate comparative chi-square distribution $p$ x $100$ percentag

test

a character string denoting the white noise test to use. Options are "port1", "port2", "port3" and "cumper" respresenting the Portmanteau I, II, III and cumulative periodogram tests, respectively. See th

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".

Value

• a list containing the level and osc vectors denoting the level and oscillation index, respectively, of the whitest transform.

concept

waveletsimulationsurrogate data generationwavelet packetsbootstrapping

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, wavBootstrap.

Examples

## calculate the DWPT of the sunspots series 
W <- wavDWPT(as.numeric(sunspots), wavelet="s8", n.levels=9)

## find the whitest transform based on the 
## Portmanteau I white noise test 
z <- wavDWPTWhitest(W, test="port1")

print(z)