A TEST FOR STATIONARITY: FINDING PARTS IN TIME SERIES APT FOR CORRELATION DIMENSION ESTIMATES

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Abstract
We propose a method to identify stationary phases in time series. Stationarity is a necessary condition for many concepts in dynamical systems theory, e.g. deterministic chaos. Therefore, testing for stationarity should necessarily be the first step in any data analysis. Above all, this testing is highly important whenever one deals with systems for which stationarity is not guaranteed by the data acquisition procedure: if only short and unique time series are accessible and if the experimental situation is not or only restrictedly controllable, as for instance in astronomy, economy, or medicine. The proposed stationarity test is easily workable and easy to implement in the form of a systematically searching loop. It singles out the parts of a time series which are a reasonable input to a dimension estimate algorithm. Thereby, it can ascertain finite correlation dimensions which are not indicative of deterministic behavior; this kind of dimensions can occur in stochastic processes which are nonstationary, e.g. self-affine.

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