# 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

1 2 |

### Arguments

`x` |
a vector containing a uniformly-sampled real-valued time series. |

`...` |
optional SDF estimation arguments passed directly to the |

`dc` |
a logical value. If |

`delta.max` |
the maximum value for the FD parameter to use in the
constrained optimization problem. Default: |

`delta.min` |
the minimum value for the FD parameter to use in the
constrained optimization problem. Default: |

`freq.max` |
the largerst normalized frequency of the SDFs use in the analysis.
Default: |

`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: |

`sdf.method` |
a character string denoting the method to use in estimating the SDF.
Choices are |

### 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

1 2 3 4 |

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