WPts {BootWPTOS}

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