Testing the Wavelet Packet Tree for White Noise

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Description

A wavelet packet tree, from the discrete wavelet packet transform (DWPT), is tested node-by-node for white noise. This is the first step in selecting an orthonormal basis for the DWPT.

Usage

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cpgram.test(y, p = 0.05, taper = 0.1)
css.test(y)
entropy.test(y)
portmanteau.test(y, p = 0.05, type = "Box-Pierce")

Arguments

y

wavelet packet tree (from the DWPT)

p

significance level

taper

weight of cosine bell taper (cpgram.test only)

type

"Box-Pierce" and other recognized (portmanteau.test only)

Details

Top-down recursive testing of the wavelet packet tree is

Value

Boolean vector of the same length as the number of nodes in the wavelet packet tree.

Author(s)

B. Whitcher

References

Brockwell and Davis (1991) Time Series: Theory and Methods, (2nd. edition), Springer-Verlag.

Brown, Durbin and Evans (1975) Techniques for testing the constancy of regression relationships over time, Journal of the Royal Statistical Society B, 37, 149-163.

Percival, D. B., and A. T. Walden (1993) Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge University Press.

See Also

ortho.basis.

Examples

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data(mexm)
J <- 6
wf <- "la8"
mexm.dwpt <- dwpt(mexm[-(1:4)], wf, J)
## Not implemented yet
## plot.dwpt(x.dwpt, J)
mexm.dwpt.bw <- dwpt.brick.wall(mexm.dwpt, wf, 6, method="dwpt")
mexm.tree <- ortho.basis(portmanteau.test(mexm.dwpt.bw, p=0.025))
## Not implemented yet
## plot.basis(mexm.tree)

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