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Rmfrac provides a collection of tools for simulating, analysing and
visualising multifractional processes and time series. The package
includes built-in estimation techniques for the Hurst function, Local
Fractal Dimension and several other geometric statistics. It provides
highly customisable plotting functions for simulated realisations,
user-provided time series and their statistics.
Features - Simulation of Brownian motion, fractional Brownian motion, fractional Gaussian noise, Brownian bridge and fractional Brownian bridge - Simulation of Gaussian Haar-based multifractional process (GHBMP) - Estimation of Hurst function and Local Fractal Dimension - Customisable plotting functions for GHBMP and user provided time series with estimates of Hurst function and Local Fractal Dimension - Estimation and visualisation of geometric statistics using realisations of stochastic processes and time series. Clustering based on the Hurst function, sojourn measure, excursion area, etc. - An interactive Shiny application that provides options to explore and visualise the core functionalities of the package through simulations and user-provided time series.
To install the development version of Rmfrac package version from GitHub:
# Install devtools if not available
# install.packages("devtools")
devtools::install_github("Nemini-S/Rmfrac")library(Rmfrac)To simulate a Gaussian Haar-based multifractional process for a constant Hurst function
t <- seq(0, 1, by = (1/2)^10)
H1 <- function(t) {return(0.5 + 0 * t)}
X1 <- GHBMP(t, H1, J = 12)Oscillating Hurst function
H2 <- function(t) {return(0.5 - 0.4 * sin(6 * 3.14 * t))}
X2 <- GHBMP(t, H2, J = 12)Piecewise Hurst function
H3 <- function(x) {
ifelse(x >= 0 & x <= 0.8, 0.375 * x + 0.2,
ifelse(x > 0.8 & x <= 1,-1.5 * x + 1.7, NA))
}
X3 <- GHBMP(t, H3, J = 12)To estimate the Hurst function and Local Fractal Dimension with visualizations
Hurst_estimates <- Hurst(X2, N = 100)
LFD_estimates <- LFD(X2, N = 100)
plot(X2, Raw_EST_H = TRUE, Smooth_Est_H = TRUE, LFD_Est = TRUE, LFD_Smooth_Est = TRUE)Ayache A, Olenko A, Samarakoon N (2025). “On Construction, Properties and Simulation of Haar-Based Multifractional Processes.” doi:10.48550/arXiv.2503.07286. Submitted, URL https://arxiv.org/abs/2503.07286.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.