Reiterated measurements of an experimentally accessible quantity of a dynami- cal system result in a time series, and one may wonder, what this information can tell about the system on which the measurements are done. Time series analysis is, thus, a very obvious way of an attempt to understand nature—already Ke- pler did it when studying the observations of Tycho Brahe. He came up with a very simple synopsis formulated in his famous laws and Newton could as- cribe these to a single law by postulating a fundamental gravitational force. This marks the beginning of modern science and then, in exploring the nature, fundamental laws or equations motivated by first principles played a dominant role.
Turning to more and more complex systems guidance by first principles be- came less fruitful for finding a mathematical model. Thus, observations cannot serve any more as indication or pointer to some fundamental underlay but have to be regarded only as a fingerprint of the system. First tasks in analyzing these fingerprints then are e.g. characterization or establishing a relation or correlation to other observations. Time series analysis in this sense, thus, has already a long history in fields where the systems to be studied are very complex such as mete- orology or medical science. Sophisticated mathematical methods appeared first in late 19th century and during the last decades these methods have been utilized also by many scientists working in applied fields. This has led to many successes in understanding complex systems.