A discrete wavelet transform of the input series is used to calculate blockdependent estimates of the FD parameter, the variance of the FD parameter and the innovations variance. Both a maximum likelihood estimation (MLE) and weighted least squares estimation (WLSE) scheme are supported. If an MLE scheme is chosen, then the DWT is used for its ability to decorrelate longmemory processes. If a WLSE scheme is chosen, then the MODWT is used for its known statistical wavelet variance properties.
1 2 3 4 5 
x 
a vector containing a uniformlysampled realvalued time series. 
boundary 
a character string representing the different methods by
which boundary wavelet coefficients and scaling coefficients
are handled in calculating the FD model parameters.
The options for this argument are dependent upon the
For the MLE case, the
For the WLSE case, the
The scaling coefficients
are (always) excluded in weighted least squares estimates
of FD model parameters. Default: 
delta.range 
a twoelement vector containing the search range for the FD parameter. Typically,
the range [10,10] is suitable for all physical systems. Default: 
documentation 
a character string used to describe the input

edof.mode 
the mode by which the equivalent degrees of
freedom are calculated. This argument is
limited to 1,2, or 3 and is used only for the WLSE scheme.
See 
estimator 
a character string denoting the estimation method. Use 
keep.series 
a logical value. If 
levels 
a vector containing the decomposition levels. The levels may be given
in any order but must be positive. Default: 
position 
a 
sdf 
a vector containing a discretized approximation
of the process spectral density function (SDF). The
coefficients of this argument should correspond
exactly with the normalized Fourier frequencies
f=0, 1/P , 2/P, 3/P, ..., (M1)/P, where
P=2*(M1) and
M is the number of points in the SDF
vector. For example, if the sdf vector contains five
elements, the corresponding frequencies will be
f=[0, 1/8, 1/4, 3/8, 1/2].
This argument is used only for the WLSE scheme when calculating EDOF mode
2 estimates. Default: 
title.data 
a character string representing the name of the input

units 
a string denoting the units of the time series. Default: 
wavelet 
a character string denoting the filter type. See 
When estimator="mle"
and
boundary="stationary"
,
the levels
vector is forced to take on
values [1,2,...,J]
where J is the maximum number of levels in a full DWT.
This is done because (in this case) the scaling coefficient and all wavelet coefficients
are used to form the FD model parameter estimates.
In using the WLSE scheme it is recommended that only the unbiased estimator be used since the confidence intervals for the biased estimator have not been sufficiently studied.
an object of class wavFDP
.
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000, 340–92.
W. Constantine, D. B. Percival and P. G. Reinhall, Inertial Range Determination for Aerothermal Turbulence Using Fractionally Differenced Processes and Wavelets, Physical Review E, 2001, 64(036301), 12 pages.
wavEDOF
, wavFDP
, wavFDPTime
, wavFDPBand
, wavFDPSDF
.
1 2 3 4 5 6  ## perform a blockaveraged MLE of FD parameters
## for an FD(0.45, 1) realization over levels 1
## through 6 using a stationarynonstationary
## FD model and Daubechies least asymmetric
## 8tap filters
wavFDPBlock(fdp045, levels=1:6, wavelet="s8", est="mle", boundary="nonstationary")

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