f noise + deterministic oscillations

Description Usage Arguments Value Warning See Also Examples

estimateFbmPars determines the fractional Brownian motion (fBm) parameters by fitting the theoretical wavelet coefficients' variances to given experimental variances. The estimation procedure is thus based on nonlinear least-squares estimates and makes use of the nls function nls.

1 2	estimateFbmPars(x, use_resolution_levels, start = NULL, lower = NULL, upper = NULL, use_weights = FALSE, algorithm = "port", ...)

`x`	A `waveletVar` object.
`use_resolution_levels`	A numeric vector specifying which resolution levels should be used in the fit.
`start`	A named list or named numeric vector of starting estimates. The names of the list should be `H` and `sigma2`.
`lower, upper`	Vectors of lower and upper bounds. Note that the `H` parameter should fulfil 0 < H < 1, whereas that `sigma2` should be sigma2 > 0 If unspecified, proper bounds are computed.
`use_weights`	Logical value indicating wheter the objective function is weighted least squares or not. If `use_weights` is `TRUE`, proper weights are automatically computed.
`algorithm`	Character string specifying the algorithm to use (see `nls`. Note that bounds can only be used with the "port" algorithm (default choice).
`...`	Additional `nls` arguments (see `nls`).

A nls object representing the fitted model. See nls for further details.

Do not use nls on artificial "zero-residual" data. See nls for further details.

waveletVar, theoreticalWaveletVar

set.seed(10)
fbm = fbmSim(n = 2 ^ 13, H = 0.4)
vpr = waveletVar(wd(fbm, bc = "symmetric"))
plot(vpr)
# Estimate the fBm parameters using the largest resolution levels
# since the estimates of their variances are better
model = estimateFbmPars(vpr, use_resolution_levels = 5:12)
# The nls-fit is performed in semilog-space. Thus, a transformation
# of the predicted values is required
points(resolutionLevels(vpr),
       2 ^ predict(model, newdata = data.frame(x = 0:12)),
       col = 2,
       pch = 2)
# Since the estimates of the largest resolution levels are better we may
# use a weigthed regression scheme
wmodel = estimateFbmPars(vpr, use_resolution_levels = 5:12,
                         use_weights = TRUE)
points(resolutionLevels(vpr),
       2 ^ predict(wmodel, newdata = data.frame(x = 0:12)),
       col = 3,
       pch = 3)
legend("topright", pch = 1:3, col = 1:3, bty = "n",
       legend = c("Original data", "nls model", "weighted-nls model"))