circFBM: Simulation of a fractional Brownian motion by using the...

In dvfBm: Discrete variations of a fractional Brownian motion

Description

Generates a discretized sample path of a fBm, B_H=(B_H(0),...,B_H(n-1/n)), at times 0,...,(n-1)/n with Hurst parameter H in (0,1) by using the circulant matrix method. A fBm with scaling coefficient C>0 and discretized at times 0,...,n-1 is obtained by the operation: n^H * C * B_H.

Usage

circFBM(n, H, plotfBm = FALSE)

Arguments

n	sample size
H	Hurst parameter
plotfBm	possible plot of the generated sample path

Details

The circulant matrix method consists in embedding the covariance matrix of the increments of the fractional Brownian motion (which is a Toeplitz matrix since the increments are stationary) in a matrix, say M, whose size is a power of 2 greater than n. One then uses general results on circulant matrices to compute easily and very quickly the eigenvalues of M. Note that the simulation fails if the procedure does not find a matrix M such that all its eigenvalues are positive.

Value

Returns a vector of length n.

Author(s)

J.-F. Coeurjolly

References

J.-F. Coeurjolly (2001) Simulation and identification of the fractional Brownian motion: a bibliographic and comparative study. Journal of Statistical Software, Vol. 5.

A.T.A. Wood and G. Chan (1994) Simulation of stationary Gaussian processes in [0,1]^d. Journal of computational and graphical statistics, Vol. 3 (4), p.409–432.

Examples

tmp1<-circFBM(500,0.2)
tmp2<-circFBM(5000,0.5)
tmp3<-circFBM(50000,0.8)

Example output

Loading required package: wmtsa

dvfBm documentation built on May 29, 2017, 9:08 p.m.