FDWhittle {fractal} | R Documentation

## 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

    set.seed(100)
    walk <- cumsum(rnorm(1024))
    FDWhittle(walk, method="discrete", sdf.method="multitaper")
    FDWhittle(walk, method="continuous", sdf.method="multitaper")

[Package fractal version 1.0-1 Index]