Time series analysis based on the smoothness measure of mapping in the phase space of attractors

As a preprocessing stage of time series prediction, an analysis of time series is an important issue since the structure of a prediction model such as delay time and embedding dimension which determine the window size, can greatly influence the performance of a prediction model. A new method of determining the optimum window size in the sense of the smoothness (or easiness) of mapping, which is defined by the given data, is suggested for the purpose of determining the structure of a nonlinear prediction model in order to be more faithfully identified to the given data. To show the effectiveness of our approach, the suggested method is applied to determining the optimum window size for the prediction of Mackey-Glass chaotic time series and analyzing ECG heart rate data