Testing the Wavelet Packet Tree for White Noise

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.

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)

Value

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

Details

Top-down recursive testing of the wavelet packet tree is

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.

Author

B. Whitcher

Examples

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)