document: Differential and integral calculus on discrete time series data It has been found that discontinuity plays a crucial role in natural evolutions -LRB- Lin 1998 -RRB- . In this presentation , we will generalize the idea of integration and differentiation , we developed in calculus , to the study of time series in the hope that the problem of outliers and discontinuities can be resolved more successfully than simply deleting the outliers and avoiding discontinuities from the overall data analysis . In general , appearances of outliers tend to mean existence of discontinuities , explosive growth or decline in the evolution . At the same time , our approach can be employed to partially overcome the problem of not having enough data values in any available time series . At the end , we will look at some real-life problems of prediction in order to see the power of this new approach
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