A Study of Improving the Coherence in Multi-Step Ahead Forecasting

The traditional multi-step ahead prediction is based on sequential algorithm to run multi-step ahead prediction and it brings error propagation problem. Furthermore, the prediction error of multi-step ahead includes both system and propagation errors. Therefore, how to decrease the propagation error has become an important issue in multi-step ahead prediction. In this study we had used the parallel algorithm to avoid the propagation error, but it brought a new problem: the incoherent learning method was used to learn the coherent time series, then, it brought an incoherent problem. Therefore, we proposed a novel parallel algorithm: after parallel algorithm, the system had to run the sequential algorithm again to avoid the incoherent problem. The experimental results evidence that the prediction error of the novel parallel algorithm was smaller than that of the parallel algorithm and the prediction error of multi-step ahead was the same as that of one-step ahead. These results imply that the prediction error of the novel parallel algorithm was approaching the system error. In addition the fractal based GP was used to learn the predicting function. The prediction error was as the radius of the trajectory line. Because the fractal was drawn by the pipe line, it indicates that the stock’s price time series belonged to the non-determinate chaos.