# WPts: Compute wavelet packet test statistic for test of... In BootWPTOS: Test Stationarity using Bootstrap Wavelet Packet Tests

## 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

 `1` ```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.

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# # 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 1, 2019, 8:47 p.m.