WPts: Compute wavelet packet test statistic for test of...
In BootWPTOS: Test Stationarity using Bootstrap Wavelet Packet Tests
WPts R Documentation
Compute wavelet packet test statistic for test of stationarity.
Description
Computes nondecimated wavelet packet transform of time series.
Computes b-spectrum (square of nondecimated WP transform) for
various levels and indices (controlled by levs and
indices arguments). Computes variance (L2 norm) of
the b-spectra and averages them. Returns the average.
Usage
WPts(x, levs, indices, filter.number = 1, family = "DaubExPhase")
Arguments
x
The time series whose statistic you want to compute.
levs
The b-spectrum levels you want to use.
indices
The b-spectrum indices you want to use.
filter.number
The filter number of the underlying wavelet.
family
The family of the underlying wavelet.
Details
Description says it all. However, the levs and
indices warrant further explanation.
Our code is designed to be used on data sets that are a power
of two, i.e. T = 2^J for some J (note: the test can work on
other values of T but coding is more finickity). Given a series of this
length there are J levels, labelled 0 (coarse) to J-1 fine. Within each
level there are J-j packets indexed 0, 1, ..., J-j-1 for scales
J-1, ..., 0 respectively.
Packet 0 within any scale always corresponds to the father wavelets
at that scale and we don't tend to use this for stationarity testing.
Packet 1 within any scale always corresponds to mother wavelets. We often
use these. Note, at the finest scale J-1 there are only two packets
0 (father wavelet) and 1 (mother wavelet) coefficients.
Value
The test statistic value is returned.
Author(s)
G.P. Nason
References
Cardinali, A. and Nason, G.P. (2016) Practical Powerful Wavelet Packet Tests
for Second-Order Stationarity. Applied and Computational Harmonic
Analysis, 2016.
doi: 10.1016/j.acha.2016.06.006
See Also
BootWPTOS
Examples
#
# Generate some test data
#
x <- rnorm(512)
#
# Compute the test statistic on mother wavelets and packets from the finest
# scale and the THIRD finest scale
#
J <- IsPowerOfTwo(length(x))
J
# [1] 9
#
x.ts <- WPts(x, levs=c(8, rep(6, 7)), indices=c(1, 1:7))
x.ts
# [1] 1.792252
BootWPTOS documentation built on May 20, 2022, 5:05 p.m.
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| WPts | R Documentation |
Compute wavelet packet test statistic for test of stationarity.
Description
Computes nondecimated wavelet packet transform of time series.
Computes b-spectrum (square of nondecimated WP transform) for
various levels and indices (controlled by levs and
indices arguments). Computes variance (L2 norm) of
the b-spectra and averages them. Returns the average.
Usage
WPts(x, levs, indices, filter.number = 1, family = "DaubExPhase")
Arguments
x |
The time series whose statistic you want to compute. |
levs |
The b-spectrum levels you want to use. |
indices |
The b-spectrum indices you want to use. |
filter.number |
The filter number of the underlying wavelet. |
family |
The family of the underlying wavelet. |
Details
Description says it all. However, the levs and
indices warrant further explanation.
Our code is designed to be used on data sets that are a power of two, i.e. T = 2^J for some J (note: the test can work on other values of T but coding is more finickity). Given a series of this length there are J levels, labelled 0 (coarse) to J-1 fine. Within each level there are J-j packets indexed 0, 1, ..., J-j-1 for scales J-1, ..., 0 respectively.
Packet 0 within any scale always corresponds to the father wavelets at that scale and we don't tend to use this for stationarity testing. Packet 1 within any scale always corresponds to mother wavelets. We often use these. Note, at the finest scale J-1 there are only two packets 0 (father wavelet) and 1 (mother wavelet) coefficients.
Value
The test statistic value is returned.
Author(s)
G.P. Nason
References
Cardinali, A. and Nason, G.P. (2016) Practical Powerful Wavelet Packet Tests for Second-Order Stationarity. Applied and Computational Harmonic Analysis, 2016. doi: 10.1016/j.acha.2016.06.006
See Also
BootWPTOS
Examples
# # Generate some test data # x <- rnorm(512) # # Compute the test statistic on mother wavelets and packets from the finest # scale and the THIRD finest scale # J <- IsPowerOfTwo(length(x)) J # [1] 9 # x.ts <- WPts(x, levs=c(8, rep(6, 7)), indices=c(1, 1:7)) x.ts # [1] 1.792252
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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