Performs test for white noise using a general wavelet decomposition of a normalized periodogram.
genwwn.test(x, away.from = "standard", lowlev = 0, plot.it = FALSE,
stopeveryscale = FALSE, filter.number = 10,
family = "DaubExPhase", mc.method = p.adjust.methods,
mac.spread = 10, verbose = FALSE)An object of class htest with the following components.
All the of unadjusted p-values
All of the adjusted p-values
The overall p-value of the test
A text string describing the test
The time series you wish to test (of dyadic length).
Number of fine scales to stay away from, see details below. If "standard" then this is automatically computed for sample sizes up to length of 1024. If you have a longer series then the test will still work but might not be quite as powerful (but probably not too bad either).
The coarsest coefficient to evaluate. This should always be left at 0.
If TRUE then a series of plots similar to the ones produced
in the hwwn.test function is produced. See that help
page for further details on what the plots show.
If TRUE then if plot.it=TRUE then a
`scan' is issued after every plot. Just hit RETURN to continue.
The number of vanishing moments of the wavelet used to compute coefficients that are then evaluated to see whether they are zero. In principle, best compression for a sparse evaluation of the normalized spectrum should mean we use the smoothest wavelets with the highest number of vanishing moments which is ten. The other components of the function are optimized for ten vanishing moments. The function will still work for other numbers of vanishing moments but maybe with slightly reduced power.
Wavelet family to go with filter.number.
The type of multiple hypothesis correction, see
p.adjust for details.
Horizontal range for plotting of wavelet coefficients,
only used if plot.it=TRUE.
If TRUE some information messages are printed.
Delyan Savchev and Guy Nason
This function computes the normalized periodogram, and then
subjects it to a wavelet transform with respect to any wavelet
(in wavethresh). Under the null hypothesis of white noise
the coefficients should all close to zero and this function
works out, for each coefficient, how close statistically it is
to zero by assuming a Gaussian null distribution with mean zero
and variance one. Then the multiple p-values from each of these
tests are adjusted for multiple hypothesis test by using the
p.adjust function before returning an overall p-value
for the test. The test has been optimized for using the
filter.number=10 wavelet and away.from="standard",
but should work pretty well for other wavelets and even away.from
values of more than 2-3 for moderate numbers of scales, and potentially
higher for longer data sets.
An approximation to the theoretical power of this test
can be obtained using the genwwn.thpower function.
Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3, 351-362. tools:::Rd_expr_doi("10.1002/sta4.69")
compute.rejection,
genwwn.thpower
#
# Generate test set, of dyadic length
#
x <- rnorm(64)
#
# Do the test:
#
answer <- genwwn.test(x)
#
# What do we get?
#
#answer
#
# Wavelet Test of White Noise
#
#data:
#p-value = 0.4629
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