Detecting switching points using asymmetric detrended fluctuation analysis

This work uses the concept of Asymmetric Detrended Fluctuation Analysis (A-DFA) to investigate and characterize the occurrence of trend switching in financial series. A-DFA introduces two new roughness exponents, H + and H − , which differ from the usual one H by separately taking into account contributions to the fluctuations according to whether the local trend is, respectively, upward or downward. The developed methodology requires the evaluation of local values of H ( t ) , H + ( t ) , and H − ( t ) , by restricting the size of the largest window around the value t . We show that H + ( t ) and H − ( t ) behave differently in the neighborhoods of switching points (SPs) where trends change sign. Properly taken differences between shifted local values of H ( t ) , H + ( t ) , and H − ( t ) allow to identify and characterize SP’s. Tests with Weiertrasse functions, isolated peaks, and actual financial series are presented, supporting the validity of the proposed method.