quadvar {FieldSim}R Documentation

Estimation of the Hurst parameter of a fractional Brownian field by the quadratic variations method

Description

The function quadvar yields the estimation of the Hurst parameter of a fractional Brownian field by the quadratic variations method.

Usage

quadvar(Z)

Arguments

Z a matrix of size (n x n). Z is the matrix associated with the sample path of one fractal Brownian field. n must be of the form 2^{J}+1 where J is a positive integer. So Z[i,j] is the value of the process at the point ((i-1)2^{-J},(j-1)2^{-J}).

Details

The Hurst parameter of the fractal Brownian field is estimated by the procedure described in Istas and Lang (1997).

Value

H a real in ]0,1[ that represents the estimate of the Hurst parameter of the fractional Brownian field.

Author(s)

Alexandre Brouste (http://ljk.imag.fr/membres/Alexandre.Brouste) and Sophie Lambert-Lacroix (http://ljk.imag.fr/membres/Sophie.Lambert).

References

J. Istas and G. Lang (1997). Quadratic variations and estimation of the local Holder index of a Gaussian process. Annales Institut Henri Poincaré *33* 407-436.

See Also

fieldsim, midpoint.

Examples

# load FieldSim library
library(FieldSim)

# Simulation
# H=0.3
res <- midpoint(H=0.3,nblevel=8)
# Estimation
quadvar(Z=res$Z)


[Package FieldSim version 1.2 Index]