  This paper reports on the application to field measurements of time series
methods developed on the basis of the theory of deterministic chaos. The major
difficulties are pointed out that arise when the data cannot be assumed to be
purely deterministic and the potential that remains in this situation is
discussed. For signals with weakly nonlinear structure, the presence of
nonlinearity in a general sense has to be inferred statistically. The paper
reviews the relevant methods and discusses the implications for deterministic
modeling. Most field measurements yield nonstationary time series, which poses
a severe problem for their analysis. Recent progress in the detection and
understanding of nonstationarity is reported. If a clear signature of
approximate determinism is found, the notions of phase space, attractors,
invariant manifolds etc. provide a convenient framework for time series
analysis. Although the results have to be interpreted with great care, superior
performance can be achieved for typical signal processing tasks. In particular,
prediction and filtering of signals are discussed, as well as the
classification of system states by means of time series recordings.
