mfsim: Simulation of Multifractal Brownian Motion

In wol-fi/multifractal: Multifractal and Surrogate Analysis

Simulation of Multifractal Brownian Motion

Description

Simulates a multifaractal Brownian motion based on Mandelbrot's "Multifractal Model of Asset Returns" (MMAR) using a lognormal cascade.

Note: the series has a length of b^k.

Usage

mfsim(b=2, k=10, H=0.5, mu=0, sigma=1)

Arguments

b	an integer representing the number of subdivision (i.e., 2 for the binomial model).
k	an integer representing the number of iterations. Note: the series has a length of b^k.
H	a numeric value within 0 and 1 denoting the Hurst exponent. This describes the persistence (i.e., level of linear auto-correlation). Above 0.5 is persistent, below 0.5 is anti-persistent.
mu	the mean value of the normal cascade.
sigma	the standard deviation of the normal cascade.

Value

Returns a simulated multifractal series.

Note

Translated from Matlab into R. Original Matlab code by Christian Wengert.

Author(s)

Wolfgang Schadner

References

Mandelbrot, B. B., Fisher, A. J., & Calvet, L. E. (1997). A multifractal model of asset returns.

See Also

mfdfa, ffGn

Examples

  # multifractal B.M.:
  B <- mfsim()
  plot(B)
  
  # multifractal noise:
  r <- diff(B)  # e.g., stock returns
  
  

wol-fi/multifractal documentation built on May 31, 2022, 1:18 a.m.