fractal (version 2.0-4)

FDWhittle: Estimate the Hurst coefficient by Whittle's method

Description

Using an estimate of the spectral density function for an input time series, Whittle's method fits the parameters of a specified SDF model to the data by optimizing an appropriate functional. In this case, the SDF for a fractionally differenced (FD) process model is used and an estimate of (\(\delta\)), the FD parameter, is returned.

Usage

FDWhittle(x, method="continuous", dc=FALSE, freq.max=0.5,
    delta.min=-1,delta.max=2.5, sdf.method="direct", ...)

Arguments

x

a vector containing a uniformly-sampled real-valued time series.

...

optional SDF estimation arguments passed directly to the SDF function. See help documentation for the SDF function for more information.

dc

a logical value. If FALSE, the DC component of the SDF (corresponding to the sample mean of the series) is not used in optimizing the Whittle functional. Default: FALSE.

delta.max

the maximum value for the FD parameter to use in the constrained optimization problem. Default: 2.5.

delta.min

the minimum value for the FD parameter to use in the constrained optimization problem. Default: -1.

freq.max

the largerst normalized frequency of the SDFs use in the analysis. Default: 0.25.

method

a character string indicating the method to be used in estimating the Hurst coefficient (H). Choices are:

"continuous"

Whittle's method using a continuous model approach to form the optimization functional. This functional is subsequently implemented via a discrete form of the SDF for an FD process.

"discrete"

Whittle's method using (directly) a discrete form of the SDF for an FD process.

Default: "continuous".

sdf.method

a character string denoting the method to use in estimating the SDF. Choices are "direct", "lag window", "wosa" (Welch's Overlapped Segment Averaging), "multitaper". See help documentation for the SDF function for more information. Default: "direct".

Value

estimate of the FD parameter of the time series.

References

M. S. Taqqu and V. Teverovsky, On Estimating the Intensity of Long- Range Dependence in Finite and Infinite Variance Time Series (1998), in A practical Guide to Heavy Tails: Statistical Techniques and Applications, pp. 177--217, Birkhauser, Boston.

See Also

hurstSpec, FDSimulate.

Examples

# NOT RUN {
set.seed(100)
walk <- cumsum(rnorm(1024))
FDWhittle(walk, method="discrete", sdf.method="multitaper")
FDWhittle(walk, method="continuous", sdf.method="multitaper")
# }