Description Usage Arguments Details Value Author(s) References See Also Examples

Uses the slope of the relationship between wavelet scale and wavelet energy to compute an estimate of the Hurst exponent

1 |

`beta` |
The estimated slope of the relationship between wavelet scale and energy. |

`model` |
The assumed long-range dependence model for the time series under analysis. |

There is a theoretical linear relationship growth in the (log) wavelet energy for increasing wavelet scale. This corresponds to the decay in the autocorrelation of a (long range dependent) time series being analysed, and therefore the Hurst exponent, H. The specific relation to H is dependent to the assumed model; in particular for a Fractional Brownian motion, the relationship between H and the slope is H = abs(beta - 1)/2, whereas for Fractional Gaussian noise or dth order Fractional differenced series, the relationship is H = (beta+1)/2.

`H` |
The Hurst exponent, computed for a specific beta and underlying model. |

Matt Nunes

Knight, M. I, Nason, G. P. and Nunes, M. A. (2017) A wavelet lifting approach to long-memory estimation. *Stat. Comput.* **27** (6), 1453–1471. DOI 10.1007/s11222-016-9698-2.

Beran, J. et al. (2013) Long-Memory Processes. Springer.

1 | ```
Hfrombeta(0.8,model="FGN")
``` |

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