Title: 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 subdiffusive and superdiffusive dynamics.