Let us finish the discussion by giving some perspectives on future work. So far, the TISEAN project has concentrated on the most common situation of a single time series. While for multiple measurements of similar nature most programs can be modified with moderate effort, a general framework for heterogeneous multivariate recordings (say, blood pressure and heart beat) has not been established so far in a nonlinear context. Nevertheless, we feel that concepts like generalized synchrony, coherence, or information flow are well worth pursuing and at some point should become available to a wider community, including applied research.
Initial experience with nonlinear time series methods indicates that some of the concepts may prove useful enough in the future to become part of the established time series tool box. For this to happen, availability of the algorithms and reliable information on their use will be essential. The publication of a substantial collection of research level programs through the TISEAN project may be seen as one step in that direction. However, the potential user will still need considerable experience in order to make the right decisions - about the suitability of a particular method for a specific time series, about the selection of parameters, about the interpretation of the results. To some extent, these decisions could be guided by software that evaluates the data situation and the results automatically. Previous experience with black box dimension or Lyapunov estimators has not been encouraging, but for some specific problems, ``optimal'' answers can in principle be defined and computed automatically, once the optimality criterion is formulated. For example, the prediction programs could be encapsulated in a framework that automatically evaluates the performance for a range of embedding parameters etc. Of course, quantitative assessment of the results is not always easy to implement and depends on the purpose of the study. As another example, it seems realistic to define ``optimal'' Poincaré surfaces of section and to find the optimal solutions numerically.
Like in most of the time series literature, the issue of stationarity has entered the discussion only as something the lack of which has to be detected in order to avoid spurious results. Taking this point seriously amounts to rejecting a substantial fraction of time series problems, including the most prominent examples, that is, most data from finance, metereology, and biology. It is quite clear that the mere rejection of these challenging problems is not satisfactory and we will have to develop tools to actually analyse, understand, and predict nonstationary data. Some suggestions have been made for the detection of fluctuating control parameters [89, 90, 91, 92]. Most of these can be seen as continuous versions of the classification problem, another application which is not properly represented in TISEAN yet.
Publishing software, or reviews and textbooks for that matter, in a field evolving as rapidly as nonlinear time series analysis will always have the character of a snapshot of the state at a given time. Having the options either to wait until the field has saturated sufficiently or to risk that programs, or statements made, will become obsolete soon, we chose the second option. We hope that we can thus contibute to the further evolution of the field.