theoreticalWaveletVar: Wavelet coefficients' variances of a fractional Brownian...

Description Usage Arguments Value See Also Examples

Description

theoreticalWaveletVar calculates the theoretical wavelet coefficients' variance of a fractional Brownian motion (fBm) with known parameters.

Usage

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theoreticalWaveletVar(H, sigma2, family, filter_number, nlevels)

Arguments

H

The Hurst exponent of the fBm.

sigma2

Variance of the fractional Gaussian noise that results after differentiating the fBm.

family

Specifies the family of wavelets used in the computation of the wavelet transform. See wd.

filter_number

An integer identifying the concrete filter used within the family of wavelets selected. filter_number is related with the smoothness of the wavelet. See wd.

nlevels

Number of resolution levels to compute. Thus, the resulting wavelet coefficients' variances are the expected ones from a fBm of length 2 ^ n.

Value

A waveletVar object with the theoretical wavelet variance.

See Also

waveletVar, estimateFbmPars

Examples

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use_H = 0.3
fbm = fbmSim(n = 2 ^ 10, H = use_H)
w_fbm = wd(fbm, bc = "symmetric")
vpr = waveletVar(w_fbm)
plot(vpr)
# the theoreticalWaveletVar also returns a 'waveletVar' object:
theo_vpr = theoreticalWaveletVar(H = use_H, sigma2 = 1,
                                 family = wtInfo(vpr)[["family"]],
                                 filter_number = wtInfo(vpr)[["filter_number"]],
                                 nlevels = length(vpr))
points(theo_vpr, col = "red")

citiususc/fracdet documentation built on May 13, 2019, 7:30 p.m.