Automated Average Cycle Length Detection in Chaotic Time Series

Fractal analysis represents a powerful tool to identify the inner dimension of various chaotic, non-linear dynamic systems. The R/S analysis, which belongs to the class of the fractal tools, can help to determine the cycles´ length of a time series, however it mostly relies on visual examination. In this paper we complement the R/S analysis with an automated method for cycles´ length detection, which is based on the Zivot-Andrews test for structural breaks. We test our method on both theoretical benchmark time series as well as real life data. We show that we can enhance the classical fractal tools with econometric techniques in order to produce an automatic procedure for cycles´ length detection, to be further used in system modeling and simulation.