Cmat.calc: Cross Autocorrelation Wavelet Inner Product Matrix...

In TrendLSW: Wavelet Methods for Analysing Locally Stationary Time Series

Cross Autocorrelation Wavelet Inner Product Matrix Calculation

Description

Internal function to compute the cross autocorrelation matrix of inner products. This is not intended for general use by regular users of the package.

Usage

Cmat.calc(
  J,
  gen.filter.number = 1,
  an.filter.number = 1,
  gen.family = "DaubExPhase",
  an.family = "DaubExPhase"
)

Arguments

J	The dimension of the matrix required. Should be a positive integer.
gen.filter.number	The index of the generating wavelet used to compute the inner product matrix.
an.filter.number	The index of the analysing wavelet used to compute the inner product matrix.
gen.family	The family of generating wavelet used to compute the inner product matrix.
an.family	The family of analysing wavelet used to compute the inner product matrix.

Details

Computes the cross inner product matrix of the discrete non-decimated autocorrelation wavelets. This matrix is used to correct the wavelet periodogram analysed using a different wavelet to the wavelet that is assumed to generate the time series. The matrix returned is the one denoted C^{(0,1)} in McGonigle et al. (2022).

Value

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

References

McGonigle, E. T., Killick, R., and Nunes, M. (2022). Trend locally stationary wavelet processes. Journal of Time Series Analysis, 43(6), 895-917.

See Also

TLSW

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