Real time series analysis in terms of predictability, entropy and chaos

Abstract

This thesis focuses on the area of time series analysis in terms of entropy, complexity, predictability and chaos. It brings five new contributions in this area, which are briefly described in separate sections and further elaborated in detail in the attached original scientific publications of the author. They include the design of accelerating modifications of the well-known approximate entropy and sample entropy algorithms, their mutual comparison, and the development of the worldwide available software TSEntropies, which enables very fast calculation of their values. The thesis also contains an explanation of the occurrence of sudden changes in these values that occur in the analysis of some time series and a suggestion of ways to prevent them. Last but not least, it also includes an examination of the relationship between the level of complexity and predictability of time series by comparing the principles of their calculation methods and the waveforms of their values. In this thesis, both artificial test time series and, most importantly, actual real time series of supercomputer infrastructure power consumption were used.