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Conclusion

We have described and to some extent justified a method to retrieve geometrical information from a one-dimensional time series by reconstructing a phase space picture of the attractor. Modifications and extensions of this method which take into account the practical problems of time series analysis have been discussed. It is important to notice that there are many different approaches to these problems and until now we do not have a general technique which can be applied to all time series. Rather than that one has to choose the technique which seems to be most appropriate for each individual data set. Further improvements of the reconstructed attractor-picture are possible, e.g. by using the tesselation method [13]. Having gone through the embedding process one can use the well-known methods to quantify the system by calculating the usual dimensions, Lyapunov exponents, etc. An interesting application of the embedding technique is the prediction of a dynamical system, using the information retrieved from a time series [9,12,16].
next up previous contents
Next: Bibliography Up: Time Series Analysis A Previous: On the Required Number   Contents
Martin_Engel 2000-05-25