FieldSim (version 2.1)

H.test: Performs Hurst parameter test for random Gaussian field

Description

The function H.test performs the test "the Hurst parameter of Z is equal to H" against the alternative hypothesis.

Usage

H.test(Z,H,alternative="two.sided",conf.level=0.95)

Arguments

Z

a matrix of size (n x n). Z is the matrix associated with the sample path of one fractional 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 $((

H

a real in ]0,1[. H is the Hurst parameter of the fractional Brownian field to be tested.

alternative

a character string specifying the alternative hypothesis, must be one of '"two.sided"' (default), '"greater"' or '"less"'.

conf.level

confidence level of the interval

Value

• A list with the following components:
• statistic
  the value of the test statistic,
• p.value
  the p-value for the test,
• conf.int
  a confidence interval for the Hurst parameter,
• gamma2
  the constant of the variance used in the test.

encoding

latin1

Details

The test is build using the asymptotic distribution of the quadratic variations given in Brouste et al. (2006)

References

A. Brouste, J. Istas and S. Lambert-Lacroix (2007). On Gaussian random fields simulations.

See Also

fieldsim, midpoint.

Examples

# load FieldSim library
library(FieldSim)

# Simulation
# H=0.3
res <- midpoint(H=0.3,nblevel=8)
# Test "H=0.3" against "H!=3"
H.test(res$Z,H=0.3)