Generate integrate fractional Brownian motion with a random noise

Source: R/generate_data.R

This function generates a realization of an integrate fractional Brownian motion with random noise. The increments of a integrate fractional Brownian motion are not independent. An integrate fractional Brownian motion is characterized by a parameter \(H\), named Hurst coefficient. We define it on \([0, 1]\).

integrate_fractional_brownian_trajectory(M, H, sigma, L = 1)

Arguments

M

An integer, expected number of points in the trajectory. The number of points follows a Poisson distribution with mean \(M\).
H

Numeric, Hurst coefficient. \(0 < H < 1\). As we return its integrated version, the true Hurst will be 1 + H.
sigma

A vector of numeric, standard deviation of the noise to add to the fractional Brownian motion.
L

Numeric, multiplicative constant.

Value

A tibble containing the following elements:

  • ...1 The sampling points

  • ...2 The true trajectory

  • ...3 The trajectory contaminated by noise with standard deviation \(\sigma\)