LFD: Estimation of the local fractal dimension

In Rmfrac: Simulation and Statistical Analysis of Multifractional Processes

Estimation of the local fractal dimension

Description

This function computes the estimates for the local fractal dimension.

Usage

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

Arguments

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

Details

The formula \widehat{LFD} = 2-\widehat{H}(t) is used to compute the estimated local fractal dimension, where \widehat{H}(t) is the estimated Hurst function.

Value

A data frame where the first column is a time sequence and the second column is estimated values of the local fractal dimension.

Note

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

References

Gneiting, T., and Schlather, M. (2004). Stochastic models that separate fractal dimension and the Hurst effect. SIAM Review, 46(2):269-282. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1137/S0036144501394387")}.

See Also

Hurst, H_LFD, plot.mp, plot_tsest, plot.H_LFD

Examples

#LFD 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)
LFD(X)


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

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