Inferring characteristic timescales from the effect of autoregressive dynamics on detrended fluctuation analysis

Exploiting recent progress in the theoretical understanding of detrended fluctuation analysis (DFA), we use the non-asymptotic properties of the fluctuation function in order to extract more information from time series data than just its Hurst exponent. In particular, we can identify exponential relaxation and oscillation periods and estimate their specific values. We illustrate the strength of this method through applications to climate data. Thereby, we determine the relaxation time of the atmospheric response to perturbations. We also find by DFA a period length of the dominant frequency mode of the El Niño Southern Oscillation to be 3.3 years.