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CONCLUSIONS AND SUGGESTIONS

We studied dimension and entropy estimators and their applicability to time series obtained from models and biological sources. In this chapter we give a summary of this study with conclusions and suggestions for future research.

Nearest neighbour methods are based on the scaling behaviour of the distances between points in phase space as a function of the neighbour index ($k$) or the number of points ($N$). We introduced a variant of this method, where the neighbour index is a function of the number of points, of the form $k = \alpha N^\beta$.

We studied the correlation integral method because it provides a good means for identifying the scaling region (that is, for the correlation dimension $\nu$) and that the form of the distribution for the distances is known ( $P(r) = \phi r^\nu$). We derived maximum likelihood estimators of the correlation dimension and entropy by using information from outside the scaling region.

We applied the maximum likelihood estimators of the correlation dimension and entropy to time series obtained from the measurements of the brain activity (electroencephalograms) and of the respiration (volume of breaths).


next up previous contents
Next: The derivatives of the Up: The identification of strange Previous: Discussion   Contents
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