Statistical test for fractional Brownian motion based on detrending moving average algorithm
arXiv:1803.08553 · doi:10.1016/j.chaos.2018.08.031
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.
References in corpus (12)
- Detrending moving average algorithm for multifractals
- Multifractal detrending moving average cross-correlation analysis
- Comparison of detrending methods for fluctuation analysis
- Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series
- Detrending Moving Average variance: a derivation of the scaling law
- Algorithm to estimate the Hurst exponent of high-dimensional fractals
- Spatio-temporal anomalous diffusion in heterogeneous media by NMR
- Detrending Moving Average Algorithm: Frequency Response and Scaling Performances
- Subordinated diffusion and CTRW asymptotics
- Effects of polynomial trends on detrending moving average analysis
- New Results on the Sum of Gamma Random Variates With Application to the Performance of Wireless Communication Systems over Nakagami-m Fading Channels
- NMR signals within the generalized Langevin model for fractional Brownian motion