Block-independent (instantaneous) estimation of fractionally differenced (FD) model parameters.

USAGE:

wavFDPTime( x, levels = 2:6, wavelet = ``s8",
      estimator = ``lse", biased = F, dof = 0 )

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 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:

, , , , .

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 )