Hfrombeta {liftLRD} | R Documentation |

## Compute Hurst exponent from wavelet scale - energy regression slope

### Description

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

### Usage

```
Hfrombeta(beta, model = c("FBM","FGN","ID"))
```

### Arguments

`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. |

### Details

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.

### Value

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

### Author(s)

Matt Nunes

### References

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.

### See Also

### Examples

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

*liftLRD*version 1.0-9 Index]