Atau.mat.calc: Lagged Autocorrelation Wavelet Inner Product Calculation

In TrendLSW: Wavelet Methods for Analysing Locally Stationary Time Series

Lagged Autocorrelation Wavelet Inner Product Calculation

Description

Internal function for computing the matrix of lagged autocorrelation wavelet inner products. This is not intended for general use by regular users of the package.

Usage

Atau.mat.calc(J, filter.number = 1, family = "DaubExPhase", lag = 1)

Arguments

J	The dimension of the matrix required. Should be a positive integer.
filter.number	The index of the wavelet used to compute the inner product matrix.
family	The family of wavelet used to compute the inner product matrix.
lag	The lag of matrix to calculate. A lag of 0 corresponds to the matrix A defined in Nason et al. (2000).

Details

Computes the lagged inner product matrix of the discrete non-decimated autocorrelation wavelets. This matrix is used in the calculation to correct the wavelet periodogram of the differenced time series. With lag = \tau, the matrix returned is the matrix A^\tau in McGonigle et al. (2022).

Value

A J-dimensional square matrix giving the lagged inner product autocorrelation wavelet matrix.

References

McGonigle, E. T., Killick, R., and Nunes, M. (2022). Modelling time-varying first and second-order structure of time series via wavelets and differencing. Electronic Journal of Statistics, 6(2), 4398-4448.

Nason, G. P., von Sachs, R., and Kroisandt, G. (2000). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(2), 271–292.

See Also

TLSW

TrendLSW documentation built on May 29, 2024, 6:06 a.m.