Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

• Our work characterizes a single exponent estimator like DFA when applied to mBm.
• DFA estimates a time averaged Hurst exponent in systems: this assertion is verified.
• We identify parameters that can impact the robustness of DFA.
• Results serve as benchmark for using DFA as sliding window Hurst exponent estimator.

The Hurst exponent (HH) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm  ) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t)H(t) as against a constant HH. Recently, there has been a growing interest in time dependence of H(t)H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA   to estimate scaling exponents in systems with time varying H(t)H(t), such as mBm. This paper characterizes the performance of DFA on mBm   data with linearly varying H(t)H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA   as a sliding window estimator to obtain H(t)H(t) from time series data.