generate_piecewise_fractional_brownian: Generate a list of piecewise fractional Brownian trajectory.

In StevenGolovkine/denoisr: Nonparametric Kernel Smoothing Methods for Functional Data

Description

This function generates a list of realizations of a piecewise fractional Brownian motion with random noise. A piecewise fractional Brownian motion is defined by a non constant Hurst parameter along the sampling points. We observe the process at regularly spaced time t_i = \frac{i}{M_n}, where i = 0, …, M_n. We define a segmentation τ = (τ_k)_{k=0, …, K+1}, with 0 = τ_0 < τ_1 < … < τ_{K} < τ_{K+1} = 1. So, on the interval [τ_k, τ_{k+1}], for k = 0, …, K, the process is a fractional Brownian motion with Hurst parameter H_k.

Usage

generate_piecewise_fractional_brownian(
  N = 100,
  M = 100,
  H = c(0.2, 0.5, 0.8),
  sigma = 0.05,
  pdf = NULL
)

Arguments

N	An integer, number of curves to simulate.
M	An integer, expected number of points in the trajectory. The number of points follows a Poisson distribution with mean M.
H	A vector of numeric, Hurst coefficients. 0 < H_k < 1
sigma	A vector of numeric, standard deviation of the noise to add to the piecewise fractional Brownian motion. Should have the length of H. It adds heteroscedastic noise to the data.
pdf	A function for the generation of the sampling points.

Value

A tibble containing the following elements:

• ...1: The sampling points

• ...2 The true trajectory

• ...3 The trajectory contaminated by noise with standard deviation σ

Examples

generate_piecewise_fractional_brownian(100, 50, c(0.2, 0.5, 0.8), 0.1)

StevenGolovkine/denoisr documentation built on Nov. 15, 2021, 8:44 a.m.