circFBM {dvfBm} | R Documentation |
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.
circFBM(n, H, plotfBm = FALSE)
n |
sample size |
H |
Hurst parameter |
plotfBm |
possible plot of the generated sample path |
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.
Returns a vector of length n
.
J.-F. Coeurjolly
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.
tmp1<-circFBM(500,0.2) tmp2<-circFBM(5000,0.5) tmp3<-circFBM(50000,0.8)