LSWPbasis: Estimate an LSWP basis by penalised least squares

In LSWPlib: Simulation and Spectral Estimation of Locally Stationary Wavelet Packet Processes

Estimate an LSWP basis by penalised least squares

Description

LSWPbasis returns a matrix containing the wavelet packet basis indices.

Usage

LSWPbasis(x, wavelet, lev.max, smooth, spa, penalty = 0.976)

Arguments

x	a (locally stationary) time series of dyadic length.
wavelet	the wavelet used to estimate the wavelet packet spectra.
lev.max	the maximum scale for which the basis is fitted.
smooth	should the penasised least squares cost functionals be smoothed? Default value is TRUE.
spa	parameter for the local polynomial smothing implemented through lowess
penalty	implemets increasing penalty for increasing scales.

Details

This function fits a wavelet packet basis to data using a penalised least square method.

This function implements a data-driven basis selection of locally stationary time series. The wavelet argument is specified as in other functions of this package. Therefore, the current implementation allows for three discrete wavelets: Haar ("haar"), Daubechies Extremal Phase linear filters of length 4 ("d4") and Least Asymmetric linear filters of length 8 ("la8"). Smoothing is controlled through the argument spa.

Value

A matrix of dimensions |b| x 2, where |b| is the number of packets in the basis. The first column contains the scale indices of each packet in the basis, the second column contains the packet index within each scale.

Author(s)

Alessandro Cardinali

References

A. Cardinali and G.P. Nason (2017). Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting. Journal of Time Series Analysis, 38:2, 151-174.

See Also

LSWPspec, LSWPsim

Examples

wpb <- LSWPbasis(x = sp500, wavelet = 'la8', lev.max = 4, smooth = TRUE, spa = 0.35)

LSWPlib documentation built on March 18, 2022, 6:55 p.m.