Instantaneous estimation of fractionally differenced model parameters
Description
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 chisquared degrees of freedom in estimating the FD model parameters.
Usage
1 2 3 4 5 
Arguments
x 
a vector containing a uniformlysampled realvalued time series. 
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: 
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

dof.order 
the degree of freedom (DOF) order. The number of
chisquare 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: 
estimator 
a character string denoting the estimation method.
Use "lse" for least squares estimates and "mle" for maximum likelihood estimates.
Default: 
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 
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 
Value
an object of class wavFDP
.
References
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.
See Also
wavFDP
, wavFDPBlock
, wavFDPBand
, wavFDPSDF
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## perform a unbiased instantaneous LSE of FD
## parameters for an FD(0.45, 1) realization
## over levels 1 through 6 using Daubechies
## least asymmetric 8tap filters. Use a zeroth
## order DOF (equivalent to 1 chisquare DOF)
z < wavFDPTime(fdp045, levels=1:6, wavelet="s8", est="lse", biased=FALSE)
## display the results
print(z)
## plot the results
plot(z)
## plot the results with the confidence intervals
## centered about the mean (known) value of the
## the FD parameter
plot(z, mean.delta=0.45)
