Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 |

`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. |

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.

The test statistic value is returned.

G.P. Nason

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.

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