The MODWT is used to calculate instantaneous estimates of the FD parameter, the
variance of the FD parameter and the innovations variance. The user can select
between maximum likelihood and least squares estimators. Localized estimates may
also be formed by using multiple chi-squared degrees of freedom in estimating
the FD model parameters.
REQUIRED ARGUMENTS:
x
A vector containing a uniformly-sampled real-valued time series.
OPTIONAL ARGUMENTS:
levels
A vector containing the decomposition levels. The levels may be given in any
order but must be positive. Default: 1:J where J is the maximum wavelet
decomposition level at which there exists at least one interior wavelet
coefficient.
wavelet
A character string denoting the filter type. See wavDaubechies for details.
Default: ``s8".
estimator
A character string denoting the estimation method. Use ``lse" for least squares
estimates and ``mle" for maximum likelihood estimates. Default: ``lse".
biased
A logical flag used to choose between denoting biased or unbiased estimates.
Biased estimates are those which use all available levels in calculating the FD
model parameters. Unbiased estimates are calculated with only those wavelet
coefficients not subject to circular filter operations, i.e. only the interior
wavelet coefficients are used in calculating unbiased estimates. Default: TRUE.
dof.order
The degree of freedom (DOF) order. The number of chi-square DOFs used in
estimating the FD parameters is equal to 2 * dof.order + 1 where necessarily
dof.order > 0. As the order increases, the estimates will become smoother but
less localized in time. Default: 0.
delta.range
A two-element vector containing the search range for the FD parameter.
Typically, the range [-10,10] is suitable for all physical systems. Default:
c(-10, 10).
VALUE:
result
An object of class WaveletFDP.
REFERENCES:
(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'',
Cambridge University Press, 2000, 340-92.
(2) 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.
SEE ALSO:
,
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,
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EXAMPLES:
## perform a unbiased instantaneous LSE of FD parameters
## for an FD(0.45, 1) realization over levels 1 through 6
## using Daubechies least asymmetric 8-tap filters.
## Use a zeroth order DOF (equivalent to 1 chi-square DOF)
result <- wavFDPTime( fdp045, levels = 1:6,
+ wavelet = "s8", est = "lse", biased = F )
## display the results
print( result )
## plot the results
plot( result )
## plot the results with the confidence intervals
## centered about the mean (known) value of the
## the FD parameter
plot( result, mean.delta = 0.45 )