fBM {LongMemoryTS}

Fractional Brownian Motion / Bridge of Type I or II.

Description

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

Usage

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.

Author(s)

Kai Wenger

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.

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)