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 $H\left(t\right),H^{+}\left(t\right)$, and $H^{?}\left(t\right)$, by restricting the size of the largest window around the value $t$. We show that $H^{+}\left(t\right)$ and $H^{?}\left(t\right)$ behave differently in the neighborhoods of switching points (SPs) where trends change sign. Properly taken differences between shifted local values of $H\left(t\right),H^{+}\left(t\right)$, and $H^{?}\left(t\right)$ 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.