A Long-term Forecasting Model For Chaotic Time Series

To solve chaotic time series long time prediction problem, there are two kinds of methods are mainly used, that is the direct forecasting method and the iterative prediction method. The iterative prediction method is more practicable. This thesis presents a continuous prediction model based on the least squares support vector machine, using one step to forecast error and to do long time prediction by iterative methods. After detailed analysis of the factors to the long time prediction error, we found that accumulated error in the one step iterative long time prediction played a decisive role to the error influence.By making theoretical deduction to the accumulated error of the iterative long-term prediction, a conclusion that the accumulated error is a nonlinear combination of the weight, one step iterative prediction error and the basis function's derivative or partial derivative.In the process of constructing the model, Weight and Step prediction error are certain items, but the kernel function can be chosen. Base on this fact two kernel function conditions that can reduce the accumulative error speed were provided. These two conditions are important reference for choosing the kernel function. The least squares support vector machine is a common method often used to make one step prediction to chaotic time series, the kernel function equals the basis function plus the basis function in the prediction method.The main contribution of this thesis is that a new kernel function——NRBF kernel function is provided. This new function meet the two conditions of choosing a basis function and conditions of Mercer kernel function. The algorithm is implemented in matlab. Three kinds of time chaotic time series produced Logistic mapping, Lorenz system and Mackey-Glass are tested. By comparing the Simulation results, the prediction steps of the prediction method of this paper had an obvious increase.