Optimum window size for time series prediction

As a pre-processing stage, the analysis of time series is an important issue, since the structure of the prediction model (including the delay time and the embedding dimension determining the window size) can greatly influence the performance of the time series prediction. For this problem, the method of reconstructing attractors based on the correlation dimension is widely used. However, the correlation dimension is not a proper tool for determining the optimum window size, since nether the proper delay time nor the embedding dimension can be determined simultaneously, and the accurate calculation of the correlation dimension is not easy, due to the difficulties involved in identifying the scaling region and the proper number of samples. In this sense, a new method of determining the optimum window size, based on the smoothness (or easiness) of the mapping defined by the given data, is suggested for the purpose of determining the nonlinear prediction model more faithfully with respect to the given data. To show the effectiveness of our approach, the suggested method is applied to identifying the optimum window size for the prediction of Mackey-Glass chaotic time series.