f noise + deterministic oscillations

Description Usage Arguments Value See Also Examples

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

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

`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.

A waveletVar object with the theoretical wavelet variance.

waveletVar, estimateFbmPars

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")