Title: Fractals in time series data: The methodological case for fractional differencing and power spectral density approaches
Authors: Matthijs Koopmans - Mercy College, USA (United States) [presenting]
Abstract: The question of whether time series data contain fractal patterns is of interest because of their non-randomness. Therefore, they need to be accounted for in the modeling stage of the analysis. Moreover, fractals are of substantive interest, as they indicate self-similarity and scale invariance. Many statistical techniques are available to detect whether time series data contain fractal patterns, including detrended fluctuation analysis, re-scaled range analysis, fractional differencing (time domain) and a variety of spectral regression approaches (frequency domain that fit linear functions to log-log power spectra). There is more variability than there should be in the fractality estimators produced by these techniques, as well as great variation in their ability to distinguish fractal variance from seasonal and short-range dependencies. This presentation uses three real datasets (river Nile flow, daily school attendance, daily birth to teens recordings), and a set of simulations with varying levels and types of short and log-range dependency to show that fractional differencing and power spectral density analysis is superior to the other techniques, provided that they are used in conjunction. The former because of its use of stepwise model comparisons to distinguish fractal from non-fractal patterns, and the latter because its power spectrums visually demonstrate scale invariance.