Time Series Nonlinear Analysis and Its Application
|School||Hunan Agricultural University|
|Keywords||Time Series SVR Geostatistics Sunspot Uniform design Nonlinear|
There are a great deal of time series data especially multi-dimensional time series data in agricultural science, such as agricultural production, the amount of pests and natural disasters. Time series which are affected by environmental factors have inherent dynamic and highly nonlinear features. It is of great significance to develop high precision time series analysis method especially for nonlinear multi-dimensional time series because prediction is the foundation for decision-making.The traditional classical multidimensional time series analysis methods are modeled linearly, such as controlled autoregressive integrating moving average (CARMA) and controlled autoregressive (CAR), but their prediction abilities are poor. The neural networks which is based on the empirical risk minimization has good nonlinear prediction ability, but falls into local minimum easily and has poor interpretation and strong empirical defects. Support vector machine (SVM) which is based on statistical learning theory has solved the local minimum, overfitting, and nonlinear problems, and has the advantage of global optimization and strong generalization ability, so support vector machine is used as the basic modeling tool in this paper.We have advanced SVR-CAR, which is a nonlinear multi-dimensional time series analysis model that compromises autocorrelation and autoregression, by combining Support vector machine regression and CAR. SVR-CAR is based on the principle of minimum mean squared error(MSE) to implement nonlinear determination of its dynamic timing characteristics (i.e., the number of the model extension order) and promotes the prediction performance greatly. But CAR’s order determined by F test and CAR-SVR’s order determined by minimum MSE have common defects:one is that the optimal order is obtained from low to high gradually is time-consuming, another is that the optimal order obtained by extending with the dependent and independent variables together is easy to cause information redundancy, while variables filtering are time-consuming and determining order is terminated before obtaining the optimal easily may reduce model’s performance.In the second chapter of this paper, GS-SVR is proposed. With high precision and fast order determination combined with prediction method, it can reflect time series’ dynamic features and the affect of environmental factors. Firstly, the multi-dimensional nonlinear time series was de-trended,then the structure are analyzed by semivariogram of geostatistics (GS) and the optimal order is determined by variable range fastly, secondly, factors are nonlinear filtered which based on the principle of minimum MSE, the redundancy information and dimension are reduced by principal component analysis, finally, the model is established on LSSVM.The two examples of agricultural science proved that GS-SVM has both highest precision and best stability among reference modles. GS-SVM is a nonlinear multi-dimensional time series analysis model that compromises analysis of time series and autoregression,can determine order fastly and accurately.Its advantages made it has a broad range of applications in the time series prediction fieldDetermine order, variable selection and training model were implemented independently in the one step prediction and the dynamic of models changes always. With the passage of time, the training sample will more and bigger and the training time which SVR takes up will not be accepted. What is more, for a given prediction step whether it is appropriate for all the historically accumulated samples to participate in training? Variable selection and training model often aim at fitting minimum MSE, while the MSE of whole sample fitting the target but recent sample not is obviously not we expected. It’s common sense that the necessity is quite a dubious to predict the current stock price comprising stock trading data of the early 90s. After all, the model parameter of many real time series system changes with time. The research of theoretical variable parameter in chaotic time series prediction shows that the simple increasing of training sample may reduce the prediction accuracy, the selection of the training set has great influence on the generalization of forecasting effect for this type of system, and the practical use research in chaotic time series prediction must solve the prediction problems in this kind of variable parameter chaotic systems. In the third chapter of this paper, a new method named SVR-UD was proposed to selecting sample of training with the example of predicting average number of sunspots. As one of solar activity manifestations, the changes of sunspots should have the strong relatedness with the time series of agriculture. Firstly, a cap of 63 the aftereffect in time series was identified by geostatistics. Secondly, for each to point, 63 SVR training models were produced, with the assistance of two factors which mixed level uniform design that based on the training sample and extension order number. Thirdly, optimal SVR model of 63 was selected for the standard that the optimal fitting results of the nearest point in front of the test point. One step independent forecasting results of 10 samples showed that SVR-UD extremely has better performance than SVR1 and SVR2. SVR-UD is used for dynamically selection extension order number of training samples, provides a new thread in chaotic time series prediction, and has a wide application prospect.