fBM function

Fractional Brownian Motion / Bridge of Type I or II.

fBM simulates a fractional Brownian motion / bridge of type I or II.

fBM(n, d, type = c("I", "II"), bridge = FALSE)

Arguments

• n: number of increments in the fractional Brownian motion.
• d: memory parameter -0.5<d<0.5. Note that d=H-1/2.
• type: either "I" or "II", to define the type of motion.
• bridge: either TRUE of FALSE, to specify whether ar fractional Brownian motion or bridge should be returned. Default is FALSE so that the function returns a fractional Brownian motion.

Examples

n<-1000
d<-0.4
set.seed(1234)
motionI<-fBM(n,d, type="I")
set.seed(1234)
motionII<-fBM(n,d, type="II")
ts.plot(motionI, ylim=c(min(c(motionI,motionII)), max(motionI,motionII)))
lines(motionII, col=2)

References

Marinucci, D., Robinson, P. M. (1999). Alternative forms of fractional Brownian motion. Journal of statistical planning and inference, 80(1-2), 111 - 122.

Davidson, J., Hashimzade, N. (2009). Type I and type II fractional Brownian motions: A reconsideration. Computational statistics & data analysis, 53(6), 2089-2106.

Bardet, J.-M. et al. (2003): Generators of long-range dependent processes: a survey. Theory and applications of long-range dependence, pp. 579 - 623, Birkhauser Boston.

Author(s)

Kai Wenger