# Statistical test for fractional Brownian motion based on detrending moving average algorithm

arXiv: https://arxiv.org/abs/1803.08553 · HTML: https://mlsanity.com/paper/1803.08553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [CINNAMON: A hybrid approach to change point detection and parameter estimation in single-particle tracking data](https://mlsanity.com/paper/2503.14253/) (2025)

## Abstract (arXiv)

Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on detrending moving average statistic and its probability distribution. Using the theory of Gaussian quadratic forms we determined it as a generalized chi-squared distribution. The proposed test could be generalized for statistical testing of any centered non-degenerate Gaussian process. Finally, we examine the test via Monte Carlo simulations for two exemplary scenarios of subdiffusive and superdiffusive dynamics.