Time series analysis of real-world complex systems - climate, finance, proteins, and physiology
Schmitt, Daniel T.
FacultiesFakultät für Naturwissenschaften
LicenseStandard (Fassung vom 03.05.2003)
In part I, we present the concept of a complex system and show that it is very useful despite the broad definition of the term. In part II, we present a wide variety of methods to characterize and quantify correlations and memory effects in time series, as well as nonlinear measures related to the Fourier phase organization. In part III, we explore several applications of the presented concepts and methods. Chapters 6 and 7 investigate climate dynamics. Wind and temperature fluctuations are not completely random but exhibit a high degree of persistence. In chapter 7, we propose to use the change in persistence of climate dynamics as a new complementary measure of climate change. We find indications that our climate has become less persistent, more erratic, and less predictable over the last century. In chapter 8, we analyze fluorescence spectra over time of a single light harvesting complex LH2. In different frequency ranges of the spectra we could identify at least two distinctly different dynamics. In chapter 9, we investigate memory effects in the volatility and directionality of high-frequency price fluctuations of major stock indices. In the chapters 10 to 12, physiological fluctuations are studied. First, we analyze the dynamics of sleep stages itself and find very interesting parallels to systems exhibiting self-organized criticality (SOC). Age related changes in heartbeat dynamics are explored in chapter 11. Even though the variability decreases significantly with age, we show that the fractal and nonlinear organization of heartbeat fluctuations remain surprisingly stable in healthy elderly compared to young subjects. Taking a closer look at heartbeat fluctuations during different sleep stages in young and elderly (chapter 12) reveals that static and dynamic measures of heartbeat dynamics show a pronounced stratification pattern across sleep stages but again remain surprisingly stable with healthy aging.
Subject HeadingsKomplexes System [GND]
Complex systems [LCSH]
Control theory [LCSH]
Sleep. Stages [LCSH]