An Automatic Method of Autoregression Part Selection for Gaussian Time Series Prediction

It is well known that the model's order has a great influence on the accuracy of the prediction and the complexity of calculation for the problem of time series autoregressive modelling. The higher the order, the more information may be contained, but the higher the computational complexity. Thus, it is practically important to find the right order to ensure an optimal trade-off. Traditional order-determination methods, such as linear autocorrelation function, and partial autocorrelation function, consider only the linear relationship among the parts in a time series and are computationally demanding to test the order one by one. To address this problem, this paper proposes a new method for auto regression (AR) part selection based on the maximal information coefficient, which can automatically determine the optimal AR part by measuring nonlinear functional relationships among various parts. In comparison with the wrapper method, much less computation time is required. Three case studies, in which Gaussian process is adopted as the regression tool, are carried out and the proposed method is compared with conventional 1-19th AR parts. Experimental results show that the proposed method improves effectively prediction accuracy while reducing the models structural complexity.