Hurst: Statistical estimation of the Hurst function

In Rmfrac: Simulation and Statistical Analysis of Multifractional Processes

Statistical estimation of the Hurst function

Description

This function computes statistical estimates for the Hurst function.

Usage

Hurst(X, N = 100, Q = 2, L = 2)

Arguments

X	Data frame where the first column is a numeric time sequence and the second the values of the process or time series.
N	Number of sub-intervals on which the estimation is performed on. Default is set to 100 sub-intervals.
Q	Fixed integer greater than or equal to 2. Default is set to 2.
L	Fixed integer greater than or equal to 2. Default is set to 2.

Details

Statistical estimation of the Hurst function is done based on the results of Ayache, A., & Bouly, F. (2023). The estimator is built through generalized quadratic variations of the process associated with its increments.

Value

A data frame of where the first column is a time sequence and second column is estimated values of the Hurst function.

Note

Since these are estimators of local characteristics, reliable results can only be obtained when a sufficiently large number of points is used.

References

Ayache, A. and Bouly, F. (2023). Uniformly and strongly consistent estimation for the random Hurst function of a multifractional process. Latin American Journal of Probability and Mathematical Statistics, 20(2):1587–1614. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.30757/alea.v20-60")}.

See Also

LFD, H_LFD, plot.mp, plot_tsest, plot.H_LFD

Examples

#Hurst function of a multifractional process simulated using GHBMP function
T <- seq(0, 1, by = (1/2)^10)
H <- function(t) {return(0.5 - 0.4 * sin(6 * 3.14 * t))}
X <- GHBMP(T, H)
Hurst(X)


#Hurst function of a fractional Browian motion simulated using FBm
X <- FBm(H = 0.5, x_start = 0, t_start = 0, t_end = 2, N = 1000)
Hurst(X)

Rmfrac documentation built on Sept. 10, 2025, 10:31 a.m.