Self-similar Models: How Close the Diffusion Entropy Analysis and the Detrended Fluctuation Analysis Are from Other Models
Financial and seismic data, like many other high frequency data are known to exhibit memory effects. In this research, we apply the concepts of Lévy processes, Diffusion Entropy Analysis (DEA) and the Detrended Fluctuation Analysis (DFA) to examine long-range persistence (long memory) behavior in time series data. Lévy processes describe long memory effects. In other words, Lévy process (where the increments are independent and follow the Lévy distribution) is self-similar. We examine the relationship between the Lévy parameter (α) characterizing the data and the scaling exponent of DEA (δ) and that of DFA (H) characterizing the self-similar property of the respective models. We investigate how close this model is to a self-similar model and prove the numerical relationship.
Kubin, William, "Self-similar Models: How Close the Diffusion Entropy Analysis and the Detrended Fluctuation Analysis Are from Other Models" (2020). ETD Collection for University of Texas, El Paso. AAI27961575.