Prediction And Application Of Nonlinear Time Series Based On Hybrid Model

In recent decades, nonlinear science has been rapidly developing. For nonlinear system in practical problems which cannot build the mathematical model directly, we can get nonlinear time series by experiment or observation methods. The nonlinear time series contain a wealth of information about dynamic system, and one method to get the features of nonlinear system is to build the nonlinear model. While the current modeling approach is often designed for a specific trend, so the effect of simulation data with single trend was fair, but the effect of actual data with multiple trends was often powerless. Therefore, we wish to build a hybrid model to catch the multiple trends, so that we can describe the dynamic system more comprehensively and accurately.This paper mainly includes the following parts:First, we optimize the BP neural network. By the minimum description length method we can solve the problems about choosing the number of the neurons in the middle layer. And by grey relational analysis on the rough sets, we can solve the problems about choosing the step of prediction.Secondly, we build the hybrid model. Through the parallel BP neural network model, the ability of catching both the long and short trends and the stability of the model are enhanced. By the way of variance power, we combine the parallel BP network and grey model that can make up for the lack of short prediction by network and long prediction by grey model. And then through the Markov process which modifies the error of first prediction, we can drop some abnormal errors and avoid jumping of errors as far as possible, so that the results of prediction can be smooth.Thirdly, we make the data simulation on the hybrid model. By the simulation data and real data, we detect and compare the accuracy of hybrid model, and so on. Through the application of the actual date, we can analyze the effectiveness of hybrid models and the necessity of major parts of the hybrid model.Finally, we put forward to a method of identification of chaos. After reconstructing the original sequence in phase space, we can get the results by extracting statistics after non-parametric prediction. Such as the correlation coefficient we used in this paper. Its trend regarding to the prediction step can be a criterion for identifying that the original sequence is either periodic or chaotic.In summary, we study the nonlinear time series, through optimizing neural network, building the hybrid model and identification of chaos. So we can grasp the trend of dynamic system more accurately, and describe the multiple trends of the dynamic system more comprehensively and reveal the nature of dynamic system more intuitively.