Philosophy of the TISEAN implementation

  A number of different people have been credited for the saying that every complicated question has a simple answer which is wrong. Analysing a time series with a nonlinear approach is definitely a complicated problem. Simple answers have been repeatedly offered in the literature, quoting numerical values for attractor dimensions for any conceivable system. The present implementation reflects our scepticism against such simple answers which are the inevitable result of using black box algorithms. Thus, for example, none of the ``dimension'' programs will actually print a number which can be quoted as the estimated attractor dimension. Instead, the correlation sum is computed and basic tools are provided for its interpretation. It is up to the scientist who does the analysis to put these results into their proper context and to infer what information she or he may find useful and plausible. We should stress that this is not simply a question of error bars. Error bars don't tell about systematic errors and neither do they tell if the underlying assumptions are justified.

The TISEAN project has emerged from work of the involved research groups over several years. Some of the programs are in fact based on code published in Ref. [2]. Nevertheless, we still like to see it as a starting point rather than a conclusive step. First of all, nonlinear time series analysis is still a rapidly evolving field, in particular with respect to applications. This implies that the selection of topics in this article and the selection of algorithms implemented in TISEAN are highly biased towards what we know now and found useful so far. But even the well established concepts like dimension estimation and noise reduction leave considerable room for alternatives to the present implementation. Sometimes this resulted in two or more concurring and almost redundant programs entering the package. We have deliberately not eliminated these redundancies since the user may benefit from having a choice. In any case it is healthy to know that for most of the algorithms the final word hasn't been spoken yet - nor is ever to be.

While the TISEAN package does contain a number of tools for linear time series analysis (spectrum, autocorrelations, histograms, etc.), these are only suitable for a quick inspection of the data. Spectral or even ARMA estimation are industries in themselves and we refer the reader - and the user of TISEAN - to the existing literature and available statistics software for optimal, up-to-date implementations of these important methods.

Some users will miss a convenient graphical interface to the programs. We felt that at this point the extra implementational effort would not be justified by the expected additional functionality of the package. Work is in progress, however, to provide interfaces to higher level mathematics (or statistics) software.