FieldSim (version 2.1)

quadvar: 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

Value

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

encoding

latin1

Details

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

References

J. Istas and G. Lang (1997). Quadratic variations and estimation of the local Holder index of a Gaussian process. Annales Institut Henri Poincar� *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)