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

Abstract

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 anomalous diffusion: subdiffusive and superdiffusive dynamics as well as for classical diffusion.