Simulation and Analysis of Multifractional Stochastic Processes with R Package Rmfrac

TL;DR

The paper introduces the Rmfrac R package for simulating, analyzing, and visualizing multifractional stochastic processes, extending classical models with variable regularity over time.

Contribution

It presents the Rmfrac package that enables simulation and analysis of multifractional processes using Haar wavelet series, including estimation and visualization tools.

Findings

The package allows simulation of multifractional time series with variable Hurst functions.

It includes functions for estimating the Hurst function and local fractal dimensions.

A Shiny app visualizes simulation and estimation results effectively.

Abstract

Brownian motion and fractional Brownian motion have been widely applied in statistical modeling in finance, telecommunication, network traffic, neuroscience, physics, and other fields. More realistic models for real time series data, such as multifractional processes, generalize these classical models by allowing their regularity to vary over time. A new class of Gaussian Haar-based multifractional processes, which utilizes the Haar wavelet series representation, was recently introduced. It significantly extends the range of available models by incorporating more general classes of Hurst functions. The Rmfrac package was developed to simulate multifractional time series. The package also comprises several functions for the analysis and visualization of time series. It includes the estimation of the Hurst function and local fractal dimension, clustering realizations and computing various geometric statistics of these time series. The package also offers a Shiny application to visualize simulation and estimation results. The article presents an overview of the Rmfrac package and exemplifies its main functionalities.